Let $f(x)=co{s}^2(x)si{n}^3(x).$

$(a)$ Use the Trapezoid Rule with $3$ equal subintervals $to$ estimate the integral $off(x)$ from

$x=-tox=\frac{}{2}.$ Show all work.

$(b)$ Use the Midpoint Rule with $3$ equal subintervals $to$ estimate the integral $off(x)$ from

$x=-tox=\frac{}{2}.$ Show all work.

$(c)$ Find the exact value $of{\displaystyle \underset{-}{\overset{\frac{}{2}}{}}}co{s}^2(x)si{n}^3(x)dx.$ Show all work.