Folland Theorem 2.15. How does this 'Let $N \to \infty$ and apply monotone convergence theorem' works?

I am reading Real analysis by Folland G.B. I have a slight doubt on this..

Theorem 2.15

If $(f_n)$ is a finite of infinite sequence in $L^+$ and $f=\sum_n f_n$, then $\int f = \sum_n \int f_n$

In the proof he proved this for $n=2$, and said that it will hold for any finite N, by induction. so $$\int \sum_{n=1}^N f_n = \sum_{n=1}^N \int f_n$$ Upto this I understood... after that he wrote $\color{red}{"\textrm{Letting $N \to \infty$ and applying the monotone convergence theorem again, we obtain} \int f = \sum_n \int f_n} $.

I wasn't able to understand the thing which is in red. How to do that precisely?