Yes, it's the usual diagram used to illustrate the integral test.
Take $f(x)=1/x$ in the following diagram.

Then $a_1=1$, $a_2=1/2$, $\ldots$. Note that in the diagram, the infinite sum is the sum of the areas of the drawn rectangles, while the integral is the area under the graph of $f$ over the interval $[1,\infty)$. Note that this integral is greater than $\sum\limits_{n=2}^\infty a_n$; so $\sum\limits_{n=1}^\infty a_n = a_1+ \sum\limits_{n=2}^\infty a_n\le a_1+\int_1^\infty f(x)\,dx.$
For the "finite version", as you have, use the same diagram; but "cut it off" at the appropriate point. You'll be able to see why your inequality holds.
(I may post a nicer diagram later; but I had this one on hand.)