What is the area of the region bounded by $y = x + 1$, the $x$-axis and the lines $x = 1$ and $x = 3$?

Explanation

1. 01

   $\int_1^{3} (x + 1)\,dx = \left[\frac{x^{2}}{2} + x\right]_1^{3}$.

2. 02

   $\left(\frac{9}{2} + 3\right) - \left(\frac{1}{2} + 1\right) = 6$ square units.