Example 7.4.7(b): Riemann implies Lebesgue Integrable
Show that the converse of the above theorem is false, i.e. not every
bounded Lebesgue integrable function is Riemann integrable.
The Dirichlet function restricted to [0, 1] is bounded and
Lebesgue integrable (with the intgral zero), while it is not Riemann
integrable.