Given the functions, f(x)=(x-2)² +3 and g(x)=x+3,

c. Write a limit expression of Riemann sums to represent the integral expression from area between the two functions

d. Determine the volume for the region bounded by f(x) and g(x) rotated about the line x=1

e. Write an expression to represent the volume for the region bounded by f(x) and g(x) rotated around the line x=-1