Get MassLynx to show you what it's integrated (there's an option somewhere for shading the relevant bit of peak). My guess is that when it repeats the same retention time, it has integrated the entire double peak as one, and it's marking each summit within the peak with the retention time that it has assigned to the whole double-peak, whereas when it integrates the two parts of the peak separately, it marks the two summits with the retention times it has assigned to the two partially-resolved peaks. But this is a total guess on my part!
By the way, I suspect you're over-smoothing some of your chromatograms with Savitzky-Golay smoothing as the option? The bottom left one in particular has a funny little downward dip either side of the peak which is characteristic of Waters' implementation of Savitzky-Golay when there is no signal and then a sudden jump up a peak. If it bothers you and messes up the integration, try an alternative.