Answer
$\displaystyle{s=-\frac{1}{3w}\cos^3wt+\frac{1}{3w}}$
Work Step by Step
$\displaystyle{s=\int f(t)\ dt}\\
\displaystyle{s=\int \sin wt\ \cos^2wt\ dt}\\
\displaystyle{s=-\frac{1}{3w}\cos^3wt+C}$
$\displaystyle{s=-\frac{1}{3w}\cos^3wt+\frac{1}{3w}}$
$s=f(0)=0\\$
$0=-\frac{1}{3w}\cos^3w(0)+C\\
0=-\frac{1}{3w}+C\\
C=\frac{1}{3w}\\$
$\displaystyle{s=-\frac{1}{3w}\cos^3wt+\frac{1}{3w}}$