Example 8. Determine the area bounded by the arc of the cosine curve from $x=-\frac{\pi}{2}$ to $x=\frac{\pi}{2}$ and the $O x$ axis.
Solution. Based on the geometric meaning of the definite integral, we conclude that the desired area is expressed by the integral

$$
S=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos x d x
$$

Evaluating this integral, we get

$$
S=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos x d x=\left.\sin x\right|_{-\frac{\pi}{2}} ^{\frac{\pi}{2}}=\sin \frac{\pi}{2}-\sin \left(-\frac{\pi}{2}\right)=1-(-1)=2 \text { (sq. units) }
$$