Question

Let f:[-3,3 ]->R defined by f(x)=5(x)+x^3,where [x]denotes the greatest integer < =x.show that this function is integrable

Answer 1

Solution:

$f$ is continuous in $[-3,3]$ everywhere.

By the Lebesgue's criterion for Riemann integrability, $f$ is integrable on 

$[-3,3]$.