How does summing peak intensities approximate peak area?

[physical101]

Hi there I have read that the area of a peak can be approximated by summing the recorded peak intensities. I can't see how this works?
If you add all the peak intensities together is not just the magnitude of their sum and not the area of the surface the peak overlays?
Someone told me that integration is just a summation of the peak intensities but is it not a summation of the peak areas at an really small interval?
Please help

 

[Edgardo]

I suppose you are talking about http://mathworld.wolfram.com/RiemannSum.html" when evaluating the area. Then you are right, you have to take into account the mesh size $$\Delta x$$.

Could it be that your mesh size equals 1? Or maybe your are only interested in the relative area of your peak? Because then if you write down the ratio

ratio = peak_Area / total_Area

the mesh size cancels and it is sufficient to add the peak intensitities.