No, as long as one partition is established, when |p| approaches infinity, any partition is established.

Prove the general idea:

Let f(P) be the sum of any points of partition P. For a partition determined by points, take the maximum and minimum values of functions in each partition respectively, and get M(P) and l (p), which is easy to know, L(P).

l(P ')& lt； = L(P)& lt； = f(P)& lt； = M(P)& lt； =M(P'), integrable.

Swed, you'd better read a book The proof in the book is much more detailed, which is found in general mathematical analysis textbooks.