Integration given incomplete graph

Question

Could someone please help me with the attached question? I tried setting up the equation for the polynomial given points, and then finding then finding the second derivative and integrating to get 35.882, but that was not correct... 

The function f has a continuous second derivative. If f (2) = f (0) use the incomplete graph of f ' to evaluate 

Points given on the graph: (0, 1), (1, 2.718), (2, 7.389)

Answer 1

points given are for f'(x)

integration by parts, u=2x+3,,,,dv=f"(x)dx

value=(2x+3)f'(x)| [zero to 2] -∫2f'(x)dx [zero to 2]

=(2x+3)f'(x)| [zero to 2] - 2f(x) [zero to 2]

=7f'(2)-3f'(0)-2f(2)+2f(0)

=7(7.389)-3,,,,f(0)=f(2)