Integral test for convergence proof Can someone help me understand this proof? 

I don't understand why 
$f(n+1) = \int_n^{n+1}{f(n+1)}$
Thank you so much and I am sorry I have nothing else to contribute as I'm fearing it is a rather basic misunderstanding. 

The variable here is $x$ not $n$, so $f(n+1)$ is regarded as a constant. Thus,
$\int_{n}^{n+1} f(n+1)dx=f(n+1)\int_n^{n+1} dx=f(n+1)[(n+1)-n]=f(n+1)$
QED.
