What is the difference between definite and indefinite integrals?

Oct 10, 2014

Indefinite integrals have no lower/upper limits of integration. They are general antiderivatives, so they yield functions.

$\int f \left(x\right) \mathrm{dx} = F \left(x\right) + C$,

where $F ' \left(x\right) = f \left(x\right)$ and $C$ is any constant.

Definite integrals have lower and upper limits of integration ($a$ and $b$). They yield values.

${\int}_{a}^{b} f \left(x\right) \mathrm{dx} = F \left(b\right) - F \left(a\right)$,

where $F ' \left(x\right) = f \left(x\right)$.

I hope that this was helpful.