$[4$ marks$]$

$($b$)$ Approximate the area under the graph of $f(x)=sin{h}^{2}x$ between $a=-1$ and $b=1$ using a Riemann sum with $3$ equally spaced steps taking $x_k,k=1,2,3$ to be the midpoint of each step.

$[5$ marks$]$

$($c$)$ Use part $($a$)$ to determine the exact value of the area under the graph of $f(x)=sin{h}^{2}x$ between $a=-1$ and $b=1.$

$[3$ marks$]$