Q: Find the area between y = x and y = x^2. Intersections: x = x^2 gives x = 0, 1. On [0,1], x >= x^2, so x is on top. Area = integral 0 to 1 of (x - x^2) dx = [x^2/2 - x^3/3] 0 to 1 = 1/2 - 1/3 = 1/6.