Correct: B
The curves intersect when x^2 = |x|. If x >= 0, then x^2 = x => x^2 - x = 0 => x(x-1) = 0 => x = 0 or x = 1. If x < 0, then x^2 = -x => x^2 + x = 0 => x(x+1) = 0 => x = 0 or x = -1. Thus the intersection points are (-1, 1), (0, 0), and (1, 1). The area is given by 2 * ∫[0 to 1] (x - x^2) dx = 2 * [x^2/2 - x^3/3][0 to 1] = 2 * (1/2 - 1/3) = 2 * (1/6) = 1/3.