Hey, guys! I'm a poor student from Nigeria. And i need your help!
I need to prove that this function is integrable (or not integrable)
Do you mean Riemann or Lebesgue integrable?
If Lebesgue then the integral would be 0 since it is only nonzero on a set with measure 0.
As for Riemann, i don't think it's integrable since you should be able to make the difference between the upper and lower sums arbitrarily large (use the fact that $\displaystyle \mathbb{Q}$ is a dense subset of $\displaystyle \mathbb{R}$)