Question

$$=\frac{1}{2}[x-\frac{1}{2n}\sin\ 2n\ x]_{-\pi}^{\pi}$$

Evaluate

$\frac{-\frac{\sin(2nx)}{n}+4e}{4}$

Factor

$\frac{-\frac{\sin(2nx)}{n}+4e}{4}$