// one channel
static int integralImage_sumRect(IntegralImage img, int x1, int y1, int x2, int y2, int channel) {
  int bottomLeft  = img.get(x1-1, y2-1, channel);
  int bottomRight = img.get(x2-1, y2-1, channel);
  int topLeft     = img.get(x1-1, y1-1, channel);
  int topRight    = img.get(x2-1, y1-1, channel);
  ret bottomRight+topLeft-topRight-bottomLeft;
}

// sum all channels
static int integralImage_sumRect(IntegralImage img, int x1, int y1, int x2, int y2) {
  ret integralImage_sumRect(img, x1, y1, x2, y2, 0)
    + integralImage_sumRect(img, x1, y1, x2, y2, 1)
    + integralImage_sumRect(img, x1, y1, x2, y2, 2);
}