Q:

Sum cells referred to by row & column numbers taken from different cells, without using VBA

My problem is quite simple but describing it is somewhat complicated.
I have four cells containing four integers, which signify row and column numbers of two cells. E.g.
     A    B
1    54   23
2    154  123

So we have two cells: 

Cell #1: row 54, column 23 and 
Cell #2 row 154, column 123.

I want to sum the contents of all cells between Cell #1 and Cell #2. Of course, I want references to cells A1, A2, B1, B2 containing the relevant values, not the actual values. Say, I want to put this sum in cell C3.
In VBA it would be simple (albeit lengthy):
Range("C3").Cells = WorksheetFunction.Sum( _
    Range(Cells(Cells(1,1),Cells(1,2)), _
        Cells(Cells(2,1),Cells(2,2))))

How to do it without VBA?
I tried something like =SUM(ADDRESS(A1,B1),ADDRESS(A2,B2)). My problem is, using ADDRESS() returns text. If I place this text in SUM(), it returns an error.

A:

[Edited - I originally misread the question]
One way to do this would be to use the OFFSET function to locate the range you want.
=SUM(OFFSET(A1,A1-1,B1-1,A2-A1+1,B2-B1+1))

OFFSET(A1,A1-1,B1-1) represents a one cell range whose row and column numbers are the values in A1 and A2. The last two parameters (A2-A1+1 and B2-B1+1) are the number of rows and columns in the new range.

