Let g(x)=0 if is rational and if is irrational. Explain why is not riemann integrable.
when taking dissections every interval contains rational and irrational points, so the lower sums are always equal to zero for every dissection but the upper sums are always greater than zero.
Bobak
edit: sorry that isn't a complete justification because the upper integral could could be arbitrary small ( i.e. ) however it is easy to show that 1 is a lower bound on the upper integral.