What is the area bounded by $y = x^2 - 1$ and the $x$-axis?

Explanation

1. 01

   The curve meets the $x$-axis at $x = \pm 1$ and lies below it in between.

2. 02

   $\int_{-1}^{1} (x^2 - 1)\,dx = - \frac{4}{3}$, so the area is $\frac{4}{3}$ square units.