Need help with deciphering calculus 2 problem

1. The problem statement, all variables and given/known data

Use substitution to show that for any continuous function f,
$$\int_0^{\pi/2} f(\sin x)\,dx = \int_0^{\pi/2} f(\cos x)\,dx.$$
2. Relevant equations
$$\cos(\pi/2-x)=\sin x$$

3. The attempt at a solution

My confusion is that f is inside the integral, and I have no idea if it would change anything.

When I do the substitution normally, I get ##\int_0^{\pi/2} f(\cos u)\,du##, but that doesn't help because it is in terms of u and not x.

Can someone help me understand this?

 

Shoot. I don't know how the formatting works on this site. The squigly line is an integrand and they all go from 0 to pi/2.