Calc AB · Unit 6 Progress Check

AP Calculus AB Unit 6 Progress Check Integration and Accumulation of Change walkthrough.

AP Calculus AB Unit 6 is integration and accumulation — the heaviest unit in the course — and the Unit 6 Progress Check MCQ covers Riemann sums, the Fundamental Theorem, and u-substitution. This walkthrough covers the question types, the traps, and how to work through them. Explanations only — no AP Classroom answer keys.

Updated August 2026Written by Mahmudul HasanFree · No signup

What Unit 6 covers

Unit 6 is Integration and Accumulation of Change. Integration and accumulation is 17–20% of the AP Calculus AB exam — the largest single unit.

Riemann sums

Left, right, midpoint, and trapezoidal approximations, and whether each over- or under-estimates.

The definite integral

Area under a curve, including signed area below the axis.

Fundamental Theorem, Part 1

Differentiating an accumulation function, with the chain rule when the bound is a function.

Fundamental Theorem, Part 2

Evaluating a definite integral using an antiderivative.

u-substitution

Reversing the chain rule, and changing the limits when the integral is definite.

Accumulation in context

Reading a definite integral of a rate as a net change, with units.

The Progress Check MCQ: what each question type tests

These are the question patterns that recur on this Progress Check, and what each one is really asking.

Over- or under-estimate?

On an increasing function a left Riemann sum underestimates and a right sum overestimates. Sketch if unsure.

FTC Part 1 with a variable bound

d/dx of an integral from a to g(x) is f(g(x)) times g′(x). The chain rule factor is the usual casualty.

u-substitution execution

Pick u, compute du, and if the integral is definite convert the limits rather than back-substituting.

Net change interpretation

The integral of a rate gives the total change over the interval, with the rate’s units times the input units.

Signed area

Regions below the axis contribute negatively. Total area needs absolute value.

The Progress Check FRQ

Unit 6 free response is often a rate-in, rate-out problem: given a rate function, find accumulated amount, a maximum, or a net change. Points come from a correct integral setup with limits, correct use of the Fundamental Theorem, and an interpretation sentence with units.

Where students lose the most points

Forgetting +C on indefinite integrals

It is a free point to lose.

Not changing limits after u-substitution

If you substitute in a definite integral, the limits must become u-values.

Dropping the chain rule in FTC Part 1

A variable upper bound that is a function of x contributes its derivative.

Confusing net change with total distance

Signed area gives net change; total requires the absolute value.

Misreading Riemann direction

Left versus right matters, and so does whether the function is increasing or decreasing.

How to work through this unit

For every accumulation problem, write the sentence “the integral of this rate gives me …” with units before computing. That sentence is usually worth a point on its own and it prevents setup errors.

Once you have finished the Progress Check, put your raw score into our AP Calculus AB Calculator to see roughly where that pace puts you on the 1–5 scale, and use the AP Calculus AB Review for the full exam format and study plan.

Frequently asked questions

Quick answers — written by humans, not a chatbot.

What does the AP Calculus AB Unit 6 Progress Check cover?

Integration and accumulation: Riemann sums, definite integrals and signed area, both parts of the Fundamental Theorem of Calculus, u-substitution, and accumulation of change in context.

Does a left Riemann sum overestimate or underestimate?

On an increasing function a left Riemann sum underestimates and a right sum overestimates. The relationship reverses for a decreasing function.

Do I have to change the limits when using u-substitution?

If the integral is definite, either convert the limits to u-values or back-substitute to x before evaluating. Forgetting to do one of the two is a common error.

Do you post AP Calculus Unit 6 answers?

No. We publish walkthroughs of the reasoning and the traps rather than AP Classroom answer keys.