Integral Test: Anticipating That Integral is Lesser Than Riemann Sum

Question

I am given the following $f(x)$ value:

$f(x) = \frac{1}{x^2+x}$

The question says that it is possible to "anticipate" that the integral of $f(x)$ would be less than the sum of the series of $f(x)$. How is it possible to determine that? Do we use a mode of comparison with a function $g(x) = \frac{1}{x}$, that has its integral value less than the sum of its series?

Answer 1

Basically you can interpret the series sum as left riemann sum from 0 to infinity as step size 1 for monotonically decreasing function so with a simple drawing you can reach a conclusion.