Definite Integration

If \(\mathrm{f}(x)\) is a function satisfying \(\mathrm{f}^{\prime}(x)=\mathrm{f}(x)\) with \(\mathrm{f}(0)=1\) and \(\mathrm{g}(x)\) is a function that satisfies \(\mathrm{f}(x)+\mathrm{g}(x)=x^2\). Then the value of the integral \(\int_\limits0^1 f(x) g(x) d x\) is