If the image is of label "A" then, you can simply do:
sum( A[] )
or, a bit more elaborated:
image img := GetFrontImage()
number integral = sum( img[] )
result("\n The intensity of the selected region in image [")
result( img.imageGetLabel() + "]:" + img.ImageGetName() + " is: ")
result( integral)
Note that this will give you the integral (or just the sum of channel-values) in raw numbers. If you have calibrated the intensity, you will have to take the calibration into account.
If - as in most cases - you just have an intensity scale but no offset, it is straight forward:
image img := GetFrontImage()
number integral = sum( img[] )
number scale = img.ImageGetIntensityScale()
number integral_cal = integral * scale
result("\n The intensity of the selected region in image [")
result( img.imageGetLabel() + "]:" + img.ImageGetName() + " is: ")
result( integral_cal )
If you also have an origin, it becomes:
image img := GetFrontImage()
number integral = sum( img[] )
number scale = img.ImageGetIntensityScale()
number origin = img.ImageGetIntensityOrigin()
number t,l,b,r
img.GetSelection(t,l,b,r)
number nChannels = r - l
number integral_cal = (integral - origin * nChannels) * scale
result("\n The intensity of the selected region in image [")
result( img.imageGetLabel() + "]:" + img.ImageGetName() + " is: ")
result( integral_cal )