Virial equation second coefficient derivation

[Aniket1]

I've been stuck over this integral for around an hour while studying the derivation of the second coefficient of the virial equation:
∫∫dx1d x2 γ(x1,x2) where γ(x1,x2) is 1 when x1 - x2 < constant.
= V∫ dx2 γ(x1,x2) where V is the integral of dx1.
Given: periodic boundary condition: x1 + V = x1
How do you justify this step?

 

[BigJDubs]

I'd be glad if someone could help.A:If you have a periodic boundary condition of the form $x_1+V=x_1$ then it implies that the integral of $dx_1$ is $V$. So you can replace $\int_{-\infty}^{\infty}dx_1$ with $V$ in the original integral.