Adding eq. (i) and (ii),
$21=\int\limits_{0}^{\frac{\pi}{2}}\bigg(\frac{\cos^{5}\text{x}}{\sin^{5}\text{x}+\cos^{5}\text{x}}+\frac{\sin^{5}\text{x}}{\cos^{5}\text{x}+\sin^{5}\text{x}}\bigg)\text{dx}=\int\limits_{0}^{\frac{\pi}{2}}\bigg(\frac{\cos^{5}\text{x}+\sin^{5}\text{x}}{\sin^{5}\text{x}+\cos{5}\text{x}}\bigg)\text{dx}$ $\Rightarrow\ \ 21=\int\limits_{0}^{\frac{\pi}{2}}1\ \text{dx}=\bigg(\text{x}^{\frac{\pi}{2}}_{0}\bigg)\ \Rightarrow21=\frac{\pi}{2}\ \Rightarrow\text{I}=\frac{\pi}{4}$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.