Let $f$ be the function defined on $\mathbb{R}$ by $f(x) = x \mathrm{e}^{x}$.\\
A primitive $F$ on $\mathbb{R}$ of the function $f$ is defined by:\\
A. $F(x) = \frac{x^{2}}{2} \mathrm{e}^{x}$\\
B. $F(x) = (x - 1) \mathrm{e}^{x}$\\
C. $F(x) = (x + 1) \mathrm{e}^{x}$\\
D. $F(x) = \frac{2}{x} \mathrm{e}^{x^{2}}$.