Answer
$1-cos(1)$
Work Step by Step
$\int_{0}^{\pi/2}cos~x~sin(sin~x)~dx$
Let $u = sin~x$
$\frac{du}{dx} = cos~x$
$dx = \frac{du}{cos~x}$
When $x = 0$, then $u = 0$
When $x = \frac{\pi}{2}$, then $u = 1$
$\int_{0}^{1} cos~x~sin(u)~\frac{du}{cos~x}$
$= \int_{0}^{1}sin(u)~du$
$= -cos~u~\vert_{0}^{1}$
$= -cos(1)-[-cos(0)]$
$= 1-cos(1)$
