Integrate : $\int \limits_0^{\pi} \large\frac{x}{a^2 \cos ^2x + b^2 \sin ^2 x}$$dx$

Question

\[\begin {array} {1 1} (a)\;\frac{\pi^2}{ab} \\ (b)\;\frac{\pi^4}{2ab} \\ (c)\;\frac{\pi^4}{ab} \\ (d)\;\frac{\pi^3}{2ab} \end {array}\]