JEE Math Practice Question

Let $$f(x)$$ be a function satisfying $$f'(x)=f(x)$$ with $$f(0)=1$$ and $$g(x)$$ be a function that satisfies $$f\left( x \right) + g\left( x \right) = {x^2}$$. Then the value of the integral $$\int\limits_0^1 {f\left( x \right)g\left( x \right)dx,} $$ is

1. A.$$e + {{{e^2}} \over 2} + {5 \over 2}$$
2. B.$$e - {{{e^2}} \over 2} - {5 \over 2}$$
3. C.$$e + {{{e^2}} \over 2} - {3 \over 2}$$
4. D.$$e - {{{e^2}} \over 2} - {3 \over 2}$$