f is not integrable because all the lower sums are 0 and all the upper sums are 1.
What about2) For define by if and if . Prove that does not converge uniformly on [0,1] but converge uniformly on [M,1] where 0<M<1.
I don't know what the pointwise limit of , so I can't go any anywhere. It would be really helpful if someone helps me how to find the pointwise limit