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.
Context Context
The Dirichlet function restricted to [0, 1] is bounded and Lebesgue integrable (with the intgral zero), while it is not Riemann integrable.

Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
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