# Show that $lim\int_{-n}^n f=\int_{\mathbb{R}} f$

I need help showing that that $$lim\int_{-n}^n f=\int_{\mathbb{R}} f$$ where $$f$$ is a nonegative measurable function. For the case that $$f$$ is integrable over $${\mathbb{R}}$$ I think I solved using Lebesgue Dominated convergence Theorem on the sequence $$f_n=f\chi_{[-n,n]}$$. I have no idea how to proceed with the case $$\int_{\mathbb{R}} f=\infty$$

Any help would be greatly appreciated