Find the area of the figure bounded by the lines: y = x² and y = x³.

Find the intersection points of the curves:
x ^ 3 = x ^ 2
x ^ 3-x ^ 2 = 0
x ^ 2 (x-1) = 0
x1 = 0 x2 = 1
Then the area of the figure S will be equal to the difference between the areas of the figures formed by the curves on the segment [0,1]:
S = ∫x ^ 2 dx -∫x ^ 3 dx = 1/2 * x ^ 3 / 0.1 -1/3 * x ^ 4 / 0.1 = 1/2 * 1 ^ 2-0-1 / 3 * 2 ^ 3 + 0 = 1 / 2-1 / 3 = 3 / 6-2 / 6 = 1/6.