Find the Area Bounded by the Curves $y=\cos x$ And $y=\cos ^{2} x$

Multiple Choice

Find the area bounded by the curves $y=\cos x$ and $y=\cos ^{2} x$ between $x=0$ and $x=\frac{\pi}{2}$ .

A) $\frac{1}{4}$
B) $4$
C) $\frac{\sqrt{2}}{2}$
D) $\frac{1}{2}$
E) $\text { none of these }$