One of the early volumes of the "Advances in Chromatography" series discussed integrators for chromatography, and the Royal Society of Chemistry published a volume entitled "Chromatographic Integration Methods."
the word integration - mathematical calculation to find the area under the peak, but in the software just draw a line at baseline of the peak to get area by integartion, here there is no math calc.
For most of the hplc chromatograms, the peaks are integrated base to base using the software like empower. But if there is some tailing in the peak shape or some shoulders if found, then we can go for split integration. Also peak purity can also be checked if the detector is a PDA(Photo Diode array detector).