Explain this inequality, related to logarithms I am trying to understand a proof of Stirling's formula.
One part of the proof states that, 'Since the log function is increasing on the interval  $(0,\infty)$, we get 
$$\int_{n-1}^{n} \log(x) dx < \log(n) < \int_{n}^{n+1} \log(x) dx$$ for $n\geq 1$.'
Please could you explain why this is true?
In particular, I am struggling to visualise this inequality graphically/geometrically.

$$\int_{n-1}^n\log(x) dx<\int_{n-1}^{n}\log( n) dx=\log(n)$$
using $\log(n)>\log(x)$ for  $n-1\leq x<n$.
Similarly:
$$\int_n^{n+1}\log(x)dx>\int_n^{n+1}\log(n)dx=\log(n)$$
