Answer
$\frac{\pi}{4}$
Work Step by Step
$\int_CF.dr=\int_0^{\pi}(1+t)sintcostdt+\int_0^{\pi}sin^2tdt$
$=[\frac{-1}{2}(1+t)cos2t+\frac{sin2t}{4}]_0^{\pi}+[\frac{t}{2}-\frac{sin2t}{4}]_0^{\pi}$
$=-\frac{\pi}{4}+\frac{\pi}{2}$
$=\frac{\pi}{4}$