Consider the area shown below. The top curve (in blue) is y=cuberoot (x) and the bottom curve (in red) is y=x^3, and we have used the notation Dy for delta y.

The top curve is

y = √x

The bottom curve is

y = x³

We are to find the area between the two curves, the limits are 0 and 1

A = ∫ (x³ - √x) dy from 0 to 1

A = x⁴/4 - (1/2) / √x |from 0 to 1

A = 0.25 square units