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Let f(x) be a function satisfying f'(x)=...

Let f(x) be a function satisfying `f'(x)=f(x)` with `f(0)=1andg(x)` be a function that satisfies `f(x)+g(x)=x^(2)`. Then the value of the integral `int_(0)^(1)f(x)g(x)dx,` is

A

`e+(e^(2))/(2)-(3)/(2)`

B

`e-(e^(2))/(2)-(3)/(2)`

C

`e+(e^(2))/(2)+(5)/(2)`

D

`e-(e^(2))/(2)-(5)/(2)`

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