What is the area bounded by $y = x^{2} - 4$, the $x$-axis and the lines $x = 0$ and $x = 2$?

Explanation

1. 01

   On $[0, 2]$ the curve lies below the $x$-axis, so the integral comes out negative: $- \frac{16}{3}$.

2. 02

   An area is never negative: it is $\left|- \frac{16}{3}\right| = \frac{16}{3}$ square units.