$\begin{align*} \int_{-\pi}^{\pi} \frac{2x ( 1+\sin x)} {1 + \cos^2 x} dx \end{align*}$ is :

Question

( A ) $\pi^2$
( B ) $zero$
( C ) $\frac{\pi^2}{4}$
( D ) $\frac{\pi}{2}$