@Sam_Axiom No need to make it so complicated. Using the interval reproduction method, let x equal pi/2 minus t, and you can immediately get that the original integral equals pi/2 divided by 2, which is pi/4.
Keeping up the image of a traditionally genius good student is exhausting, so I think that's why I moved out of the dorm—I can't handle sharing a cramped space with others when my mind is so restless and my desires so chaotic😇