Notice through a geometric argument that
$$\int_0^af(x)\ dx=\int_0^af(a-x)\ dx$$
Now compute the following integral:
$$\int_0^{\pi/2}\frac{\sin^n(\theta)}{\sin^n(\theta)+\cos^n(\theta)}\ d\theta$$
Notice through a geometric argument that
$$\int_0^af(x)\ dx=\int_0^af(a-x)\ dx$$
Now compute the following integral:
$$\int_0^{\pi/2}\frac{\sin^n(\theta)}{\sin^n(\theta)+\cos^n(\theta)}\ d\theta$$