Convergence of Riemann sums with partitions with equidistant points

Question

I am reading Spivak's book "Calculus". The definition of integrable given there is the following:

$L(f,P)$ and $U(f,P)$ are the lower sum and the upper sum of $f$ for partition $P$.

I understand that it is a classic definition of integrable function but not the only one. For example, another definition is given in this question: Riemann sums with equidistant sample points converge to the integral

In the same book I mentioned before I found the following exercise:

Part a) has not been a problem. However, I cannot build the example requested in part b).

Could you give me any suggestion to solve this problem. Thank you very much in advance.

Answer 1

I find the following result in the book Real Analysis by Claude Warnick. The definition of integrable given there is similar to the one given in Spivak's book. So, I think there is something wrong in the statement of exercise b.