Answer
$18$
Work Step by Step
$\int_{-3}^{3}\int_{0}^{\frac{\pi}{2}}(y+y^2\cos x)\, dx\,dy=\int_{-3}^{3}\biggl[yx+y^2\sin x\biggr]_{0}^{\frac{\pi}{2}}\, dy=\int_{-3}^{3}\frac{y\pi}{2}+y^2\, dy=\biggl[\dfrac{y^2\pi}{4}+\dfrac{y^3}{3}\biggr]_{-3}^{3}=18$
