Answer
$$A = 1$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = \cos x,{\text{ }}\left[ {\pi /2,{\text{ }}\pi } \right] \cr
& {\text{From the graph we can see that the area is given by}} \cr
& A = \int_{\pi /2}^\pi {\left( {0 - \cos x} \right)} dx \cr
& A = \int_\pi ^{\pi /2} {\cos x} dx \cr
& {\text{Integrate and evaluate}} \cr
& A = \left[ {\sin x} \right]_\pi ^{\pi /2} \cr
& A = \sin \left( {\frac{\pi }{2}} \right) - \sin \left( \pi \right) \cr
& {\text{Simplifying}} \cr
& A = 1 \cr} $$
