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.

This because on $[n-1,n]$, we have $\,\ln x<\ln n\,$ except at the end point so that by the monotonicity property of the integral:
$$\int_{n-1}^n \ln x,\mathrm d\mkern1.5mux<\ln n\,[n-(n-1)]=\ln n.$$
Similarly for the other inequality.
