JEE Math Practice Question

If $\mathrm{I}=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \mathrm{~d} x$, then $\int_0^{2I} \frac{x \sin x \cos x}{\sin ^4 x+\cos ^4 x} \mathrm{~d} x$ equals :

1. A.$\frac{\pi^2}{12}$
2. B.$\frac{\pi^2}{4}$
3. C.$\frac{\pi^2}{16}$
4. D.$\frac{\pi^2}{8}$