How can I integrate the area under a curve (from experimental data) with X & Y boundary conditions?

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Hello,
How can I integrate the area under a curve (from experimental data) with X & Y boundary conditions?
My example is from chronoamperometry data (current vs time). Periodically the current will spike due to experimental conditions. I would like to integrate the area under a peak (ideally each peak) but I would like to set X & Y boundary conditions (?) so as to integrate a portion of the peak area [see attached image]. For example, in the image with green dots (my points to pick boundaries) I would like to integrate between (X1 & X2 and Y1 & Y2).
Using both trapz and cumtrapz functions, I haven’t been able to figure out how to get only my area of interest. Instead, I get the whole area under a peak [see other image with giant-"X"]. To date, the closest I’ve found to an answer appears to be from here: http://www.mathworks.com/matlabcentral/answers/122644-how-to-calculate-partial-area-under-the-curve However, I haven’t been able to figure out something that works with my data [attached].

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KSSV
KSSV 2016-9-15
Use trapz....
check the link:
https://in.mathworks.com/matlabcentral/answers/154089-area-under-curve-no-function

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