Integrate $I= \int \limits_{-\pi}^{\pi} \large\frac{\cos ^2 x}{1+a^x}$$dx$

Question

$$\begin {array} {1 1} (a)\;\frac{3 \pi}{4} \\ (b)\;\frac{\pi}{3} \\ (c)\;\frac{\pi}{2} \\ (d)\;\frac{2 \pi}{3} \end {array}$$