(f*g)(x)=\int_{-\infty}^\infty f(t)g(x-t)\,dt=\int_{-\infty}^xf(t)\,dt=\left\{
\begin{array}{ll}
0, & x<-2,
\vspace{0.5em}\\
x+2, & -2\leq x<1,
\vspace{0.5em}\\
5-2x, & 1\leq x<2,
\vspace{0.5em}\\
3-x, & 2\leq x<4,
\vspace{0.5em}\\
-1, & x\geq 4.
\end{array}
\right.