# How do you find the antiderivative for the absolute value function f(x) = |x|?

If $x \ge 0$, than $| x | = x$ and $F \left(x\right) = \int x \mathrm{dx} = {x}^{2} / 2 + c$.
If $x < 0$, than $| x | = - x$ and $F \left(x\right) = \int - x \mathrm{dx} = - {x}^{2} / 2 + c$.