$($a$)$ Using the partial fractions, evaluate the integral

$(8$ marks$)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{y-2}{(y^2+3y+2)}dy$

$($b$)($i$)$ Find $x-$intercepts of the curve $y=x^2-4.$

$(4$ marks$)$

$($ii$)$ Find the area bounded by the curve $y=x^2-4$ and the x $-$axis by the following formula:

Area $={\displaystyle \underset{a}{\overset{b}{}}}ydx$

where a and $b$ are the x $-$intercepts obtained in part $($b$)($i$)$

$(8$ marks$)$