Show that $\displaystyle ln5 < 1 + 1/2 + 1/3 + 1/4.$ using integrals

I guess....First I have to show that the integral from 1 to 5 of $\displaystyle \frac {1}x$ is equal to $\displaystyle ln(5)$.

Then estimate the integral by a finite sum of left endpoints.

Since 1/x is decreasing from 1 to 5, the finite sum I get will be strictly greater than the integral.

But I don't know how to show the steps....

How do I show that the integral from 1 to 5 of $\displaystyle \frac {1}x$ is equal to $\displaystyle ln(5)$?

How do I estimate the integral by a finite sum of left endpoints?