Lebesgue Criterion for Riemann Integrability

[quasar987]

There's a theorem in my real analysis textbook that says

A function f is Riemann-integrable iff the set of its points of discontinuity is of measure zero.But take say f(x)=1/x. It is only discontinuous as x=0, but it's not integrable on (-e,e).

 

[slearch]

i could be wrong but i think that theorem only applies to bounded functions.

 

[Crosson]

This looks like a blatant omission of the word "bounded".