Definite integrals: F(b) − F(a)

For a definite integral, find an antiderivative $F(x)$, then subtract its value at the lower limit $a$ from its value at the upper limit $b$.

$C$ cancels in the subtraction, so it is not needed. Sign mistakes are common, so write $F(b)$ and $F(a)$ separately before subtracting.

Examples

1. 01What is this definite integral?$\displaystyle \int_{1}^{2} 2x \, dx$AnswerHide

   Answer$\displaystyle 3$
2. 02What is this definite integral?$\displaystyle \int_{-1}^{1} 3x^2 \, dx$AnswerHide

   Answer$\displaystyle 2$
3. 03What is this definite integral?$\displaystyle \int_{-1}^{3} 2x \, dx$AnswerHide

   Answer$\displaystyle 8$
4. 04What is this definite integral?$\displaystyle \int_{-3}^{-1} 2x \, dx$AnswerHide

   Answer$\displaystyle -8$
5. 05What is this definite integral?$\displaystyle \int_{0}^{1} 3x^2 \, dx$AnswerHide

   Answer$\displaystyle 1$
6. 06What is this definite integral?$\displaystyle \int_{-1}^{0} 3x^2 \, dx$AnswerHide

   Answer$\displaystyle 1$

FAQ

Q1What if I swap the upper and lower limits?Show answerHide

A

The sign flips: $\int_b^a f(x)\,dx=-\int_a^b f(x)\,dx$.

Practice this pattern in the app, 5 problems a day.

Published 2026-09-03 · Updated 2026-09-05