We consider the functions $f(x) = x\mathrm{e}^{1-x^{2}}$ and $g(x) = \mathrm{e}^{1-x}$.
\begin{enumerate}
\item Find a primitive $F$ of the function $f$ on $\mathbb{R}$.
\item Deduce the value of $\int_{0}^{1} \left(\mathrm{e}^{1-x} - x\mathrm{e}^{1-x^{2}}\right) \mathrm{d}x$.
\item Give a graphical interpretation of this result.
\end{enumerate}