The figure shows the profile of a trench dug across a road. It follows the curve $y = x^2 - 1$ for $-2 \le x \le 2$, with $x$ and $y$ in metres. The road crew wants the total area between the profile and the line $y = 0$, counting the parts above and below the line as positive. What is this total area, in square metres?

Fig. 1: The blue parabola y = x squared - 1 for x from minus 2 to 2. It crosses the x-axis at minus 1 and 1. The regions between the curve and the axis are shaded: from minus 2 to minus 1 above the axis in green, from minus 1 to 1 below the axis in red, and from 1 to 2 above the axis in green.