$[$FTC$3*]($Section $5\mathrm{.}2)$ Use the area of regions in the graph below to find the following.

a$.$ Determine the value of the definite integral ${\displaystyle \underset{1}{\overset{3}{}}}\sqrt[\phantom{2}]{4-(x-3{)}^2}dx.$

b$.$ Determine the value of the definite integral ${\displaystyle \underset{1}{\overset{3}{}}}-\sqrt[\phantom{2}]{4-(x-3{)}^2}dx.$

c$.$ Determine the value of the definite integral ${\displaystyle \underset{1}{\overset{3}{}}}5\sqrt[\phantom{2}]{4-(x-3{)}^2}dx.$

d$.$ Determine the value of the definite integral ${\displaystyle \underset{3}{\overset{1}{}}}\sqrt[\phantom{2}]{4-(x-3{)}^2}dx.$