Because the integral of f(x) from 0 to a is not always f(a - x). That's dependent on what f is.
I'm pretty sure. Been many a year since I've taken Calculus, and I sure as Hell don't give a damn to do any more trig functions. If you wanna give me a Cal problem that doesn't involve trig functions, sure. I love math, 'cause it doesn't involve memorizing. Trig functions seemed like they were always about memorizing...