How is this derived? In my textbook I find the following derivation:
$$ \displaystyle \lim _{n \to \infty} \dfrac{1}{n} \displaystyle \sum ^n _{k=1} \dfrac{1}{1 + k/n} = \displaystyle \int^1_0 \dfrac{dx}{1+x}$$
I understand that it's $\displaystyle \int^1_0$ but I don't understand the $\dfrac{dx}{1+x}$ part. 

The sum $\dfrac{1}{n}  \sum\limits ^n _{k=1} \dfrac{1}{1 + \frac{k}{n}}$ is a Riemann sum of the function $f(x)=\dfrac{1}{1+x}$  with respect to the partition $0<\dfrac{1}{n}<\dfrac{2}{n}<\ldots<\dfrac{k}{n}\ldots<\dfrac{n}{n}=1.$
