What is the area of the region bounded by the line $y = 3 - x$, the $x$-axis and the lines $x = 0$ and $x = 5$?

Explanation

1. 01

   The line crosses the $x$-axis at $x = 3$: it is above the axis for $0 \le x < 3$ and below it for $3 < x \le 5$.

2. 02

   $\int_0^{3} (3 - x)\,dx + \left\lvert \int_3^{5} (3 - x)\,dx \right\rvert = \frac{9}{2} + 2 = \frac{13}{2}$ square units.