The theorem says that a function defined on a closed interval is Riemann integratble if and only if it is almost eveywhere continous. But maybe you did not do that theorem and are asked to show that a bounded ,defined almost discontinous function is not Riemann integrable. If thus, here is something that might help http://www.mathhelpforum.com/math-he...stion-4-a.html. The trick here was to subdivide the the region into rational and then irrational points.