I'd like to know the proof of this formula

$$ \int\_0^{\infty} \, e^{-a^2x^2} \operatorname{erf}(bx) \, dx=\frac{1}{a\sqrt{\pi}}\arctan{\frac{b}{a}}$$

where $\operatorname{erf}(x)$ is the error function
$\operatorname{erf}(x):=\frac{2}{\sqrt{\pi}}\int\_0^{x} e^{-y^2} \, dy$.