How to resize a Summed Area Table/Integral Image?
Calculation of the integral image is a linear transform on the original image.

Now, assuming you wanting to downscale the integral image means that you want the result to be the same whether you:


downscale the original image, integrate after
integrate the original image, downscale after


and remember that "downscaling" by a factor of $N$ the original image means


applying a low-pass filter to avoid aliasing and
throwing away $N-1$ of every $N$ pixels.


since low-pass filtering is also a linear operation, we can just switch orders of summations and down-scale the result image. Nothing special applies.