Integrate : $\int \limits_0^{\large\frac{z}{2}}$$ \cos x \sin ^3 x dx$

Question

\[\begin {array} {1 1} (a)\;\frac{z}{2} \\ (b)\;\frac{z}{4} \\ (c)\;\frac{1}{4} \\ (d)\;\frac{1}{2} \end {array}\]