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

Explanation

1. 01

   The region lies below the $x$-axis, for $0 \le x \le 3$: $\int_0^{3} (x - 3)\,dx = -\frac{9}{2}$.

2. 02

   An area is never negative: $\left\lvert -\frac{9}{2} \right\rvert = \frac{9}{2}$ square units.