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Let F:RrarrR be a thrice differentiable ...

Let `F:RrarrR` be a thrice differentiable function. Suppose that F(1)=0, F(3)=-4 and `F'(x)lt0` for all `x in (1//2,3)`. Let f(x)=xF(x) for all `x in R`.
If `int_1^3x^2F'(x)dx=-12` and `int_1^3x^3F''(x)dx=40`, then the correct expression(s) is (are)

A

9f'(3) +f'(1) -32=0

B

`int_1^3f(x) dx =12`

C

9f'(3)-f'(1) +32=0

D

`int_1^3f(x) dx=-12`

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