If you enter your start range and end range row numbers in 2 cells, say J1 and J2 then you can use the Index() function to convert that to cell addresses.

e.g. if you want to Sum cells from A1 to A10 and you put 1 in J1 and 10 in J2, then the formula would be:

=SUM(INDEX(A:A,J1):INDEX(A:A,J2))