Use the following functions to answer each question below. $(5$ points each$)$

$f(y)=(y-1{)}^{2}2$ and $g(y)=6$

a$)$ Sketch a graph for the region bounded by the functions $r$ and $g$ and determine the point$(s)$ of intersection.

b$)$ Find the area of the region between the functions by integrating over the $y-$axis.

c$)$ Find the volume when the region between the functions is revolved about the line $y=-1.$

d$)$ Set$-$up an integral to represent the volume for a solid formed whose base is the region bounded by the function $f$ and $g,$ using cross sections of squares perpendicular to the $y-$axis

e$)$ Let the line given by $h(x)=x-3$ intersect $f(y)$ and $g(y).$ Find the area bounded above by $h(x),$ bounded to the right by $g(y),$ and bounded below by $f(v).$