Answer $35$ ONLY

Compute the area bounded by the graph of $f(x)=\frac{1}{x^3},$ the $x-$axis, and the two lines $x=-2$ and $x=-1.$ Make a drawing. $($Hint: $f(x)<mn>0</mn>$ in $-2,-1.)$

Compute the area bounded by the graph of $f(x)=\frac{1}{2}(e^x+e^{-x}),$ the $x-$axis, and the lines $x=-1$ and $x=1.$

$($SM$)5.$ Evaluate the following integrals:

$($a$){\displaystyle \underset{0}{\overset{1}{}}}xdx$

$($b$){\displaystyle \underset{1}{\overset{2}{}}}(2x+x^2)dx$

$($c$){\displaystyle \underset{-2}{\overset{3}{}}}(\frac{1}{2}{x}^2-\frac{1}{3}{x}^3)dx$

$($d$){\displaystyle \underset{0}{\overset{2}{}}}(t^3-t^4)dt$

$($e$){\displaystyle \underset{1}{\overset{2}{}}}(2t^5-\frac{1}{t^2})dt$

$($f$){\displaystyle \underset{2}{\overset{3}{}}}(\frac{1}{t-1}+t)dt$