# What is an anti-derivative?

The anti-derivative (also called the integral) of a function $f$ is a function $g$ with the property that its derivative $g '$ equals the original function $f$.
ie. $\int f \left(x\right) \mathrm{dx} = g \left(x\right) + C \iff g ' \left(x\right) = f \left(x\right)$