Q: Evaluate the integral from 0 to pi/2 of sin x / (sin x + cos x) dx. Call it I. Property: integral 0 to a of f(x) = integral 0 to a of f(a-x). I = integral 0 to pi/2 of cos x / (cos x + sin x) dx (replace x by pi/2 - x). Add: 2I = integral 0 to pi/2 of 1 dx = pi/2. So I = pi/4.