These are also related to "Integral Images" or "Summed Area Tables" [1] which are used in computer vision and graphics (resp.) for many purposes (most prominently in the Viola-Jones face detector). The benefit is that taking the sum of any axis-aligned rectangle becomes a constant time operation:

  sum = bottom right - top right - bottom left + top left 

(if numbering starts from top-left). You can also compute variances in constant time this way by summing squares of numbers, etc.

[1] http://en.wikipedia.org/wiki/Integral_image