The PDF of the half-normal distribution is:
$$f(x;\sigma)=\frac{\sqrt{2}}{\sigma\sqrt{\pi}}\exp\left(-\frac{x^2}{2\sigma^2}\right)\,\quad x>0\,.$$
The integral $$\int_{0}^{\infty}f(x;\sigma)\mathrm{d}x=\int_{0}^{\infty}\frac{\sqrt{2}}{\sigma\sqrt{\pi}}\exp\left(-\frac{x^2}{2\sigma^2}\right)\mathrm{d}x$$
should be equal to one. The code used to check this:
Integrate[(Sqrt[2/Pi]/s)*Exp[-(x^2)/(2*s^2)], {x, 0, Infinity},
Assumptions -> Re[s^2] > 0]
Mathematica gives $\frac{1}{\sqrt{\sigma}}$ which doesn't make sense. What am I doing wrong?