Integrate : $\int \limits_0^{\frac{\pi}{2}} \large\frac{\phi(x)}{\phi (\Large\frac{\pi}{2}-x)+\phi (x)}$$dx$

Question

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