A trough has a flat lid along the line $y = -2$ and a curved floor along $y = x^2 - 11$, with lengths in metres, as in the figure. The cross-section is the shaded region between the lid and the floor. What is its area?

Fig. 1: A parabola y = x squared - 11, in blue, with its lowest point at height -11, and a horizontal orange line y = -2. They cross at the red dots (-3, -2) and (3, -2). The region between them, which lies entirely below the x-axis, is shaded.