# Riemann integration

Which of the following conditions are necessary for a function f to be Riemann integrable on the closed interval [a,b], where a < b?

I. f is bounded on [a,b].

II. f is continuous on [a,b].

III. f is differentiable on [a,b].

https://brainmass.com/math/integrals/riemann-integration-fractions-32641

#### Solution Preview

The answer is A. None of them are necessary.

I. f is bounded on [a,b].

This is not necessary. Here is an example. f(x)=1/sqrt(|x|) on the ...

#### Solution Summary

This discusses the requirements for Riemann integrability.

$2.19