Indefinite Integration

If $\int \mathrm{e}^{x^2} \cdot x^3 \mathrm{dx}=\mathrm{e}^{x^2} \mathrm{f}(x)+\mathrm{c}$ and $\mathrm{f}(1)=0$ (where c is a constant of integration), then the value of $f(x)$ is