Let f(x) = |x - 1|, g(x) = [x] and h(x) = f(x)g(x) where [.] is greatest integer function. What is ∫_0^2 h(x) dx equal to?

Split into [0,1) and [1,2). On [0,1): [x] = 0, so h(x) = 0. Integral = 0. On [1,2): [x] = 1, |x-1| = x-1, so h(x) = x - 1. ∫_1^2 (x-1) dx = [(x-1)²/2]_1^2 = 1/2 - 0 = 1/2. At x = 2, [2] = 2 but it's a single point. Total = 0 + 1/2 = 1/2.