Definite integrals are integrals that have limits. Limits appear in pairs; a number to the right of the top of the integral a number to the right of the bottom of the integral, such as in the following:.

$\int_a^b f(x)\, dx$

# Definite Integrals

Integration where limits are involved.

Example – $\int^3_0 x^2\, dx=\left[\frac{1}{3}x^3\right]^3_0=\left(\frac{1}{3}(3)^3\right)-(\frac{1}{3}(0)^3)=9-0=9.$

You might wonder why the integration constant is left off; this is because it cancels when evaluating definite integrals.

# Indefinite Integrals

Integration where limits are not involved.

Example – $\int x^2\, dx=\frac{1}{3}x^3+c$