When basic algebra meets calculus, chaos ensues! The first guy assumes subtracting identical integrals (∫cos(x)dx - ∫cos(x)dx) should equal zero, which makes logical sense. But calculus has other plans! Each integral actually equals sin(x) + C, where C is that infamous "constant of integration." So when you subtract them, you get (sin(x) + C₁) - (sin(x) + C₂) = C₁ - C₂, which equals some constant! The sheer mathematical betrayal on that man's face is every student who's ever been blindsided by a sneaky integration constant. That moment when you realize math wasn't playing by the rules you thought it was!