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

Let `f(x)` be a function satisfying `f'(x)=f(x)`, `f(0)=1` and `g` be a function satisfying `f(x)+g(x)=x^(2)` then `int_(0)^(1)f(x)g(x)dx` equals

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

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

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

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

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