Integrate a periodic piecewise function

$f(x)=xe^x$ for $0<x\le1$, and $f(x)=e(2-x)$ for $1<x\le2$. Also $f(x)=f(x+2)$ for all real $x$.

(i) Sketch $y=f(x)$ for $-2<x\le4$.

(ii) Find $\displaystyle\int_{-1}^{3}f(x)\,dx$ exactly.