12.53 Given the function $f(x)=|x|$. Write the expression for the antiderivative of the function.
12.53 If $x \geq 0$, then $f(x)=x$ and $F(x)=0.5 x^{2}+C$; if $x<0$, then

$$
f(x)=-x \text { and } F(x)=-0.5 x^{2}+C
$$