What is the area of the region bounded by the line $y = 2x + 1$, the $x$-axis and the lines $x = 0$ and $x = 3$?

Explanation

1. 01

   $\int_0^{3} (2x + 1)\,dx = \left[x^{2} + x\right]_0^{3}$.

2. 02

   $9 + 3 = 12$ square units, a trapezium with parallel sides 1 and 7.