Find the Area Bounded by the Curves $y = \cos x$

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) none of these