The value of $\begin{align*} \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin^2 x}{1+2^x} dx \end{align*}$ is :

Question

( A ) $\frac{\pi}{2}$
( B ) $\frac{\pi}{4}$
( C ) $\frac{\pi}{8}$
( D ) $4 \pi$