Find the $$\lim_{c \to \infty} \int_{-\infty}^{\infty} |g(x) - g(x+c)|dx$$ where $g$ is integrable.
I know already that if $g$ is integrable, than the integral of $g(x)$ and the integral of $g(x+c)$ are equal, so I thought perhaps that will help. But to use this I think I would need to split up the integral into two pieces.