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

Let f(x) be a function satisfying`f'(x)=f(x)` with`f(0) =1` and g(x) be a function that satisfies `f(x) + g(x) = x^2` . Then the value of the integral `int_0^1f(x) g(x) dx`, is

A

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

B

`e-e^(2)-3`

C

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

D

`e-(1)/(2)e^(2)-(3)/(2)`

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