What is the area of the region bounded by $y = x^{2}$, the $x$-axis and the lines $x = 1$ and $x = 2$?

Explanation

1. 01

   $\int_1^{2} x^{2}\,dx = \left[\frac{x^{3}}{3}\right]_1^{2}$.

2. 02

   $\frac{8}{3} - \frac{1}{3} = \frac{7}{3}$ square units.