The figure shows the curves $y = x^2$ and $y = x^3$ for $0 \le x \le 1$. They meet at the origin and at $(1, 1)$. What is the area of the shaded region between them?

Fig. 1: The curves y = x squared, in blue, and y = x cubed, in orange, between x = 0 and x = 1. They meet at (0, 0) and (1, 1). The thin region between them is shaded. The parabola is above the cubic.