Matlab and integrating under area of Gaussian curve for lab experiment

This is going to be a long post due to information that I am going to have to present.

A brief outline in what I am asking is, that I need to integrate a Gaussian at a specific height above the x-axis so I don't want all the integration just a certain part under the curve. I have written the code to which I believe is integration all the values under the curve which I dont not want.

Here all data and full explanation with code.

So my lab experiment is on gamma ray spectroscopy and I need to find the amount of counts underneath the curve, now this was done on a program called cassy, where we could highlight the area and it would calculate this or us, but due to a miss hap one of the data plot was not integrated correctly so I am trying to do it on matab.

Starting with a count I have already integrated and a total count of $529$ for I will use this as an example.

Actual graph of data/code

The red portion is what I am trying to integrate.

Matlab code:

dataset = xlsread('Lab 3 Results 11.10.18 (1).xlsx','Sheet3','C4:D515');

x=dataset(:,1);

y=dataset(:,2);

plot(x,y)

So because of the random decay pattern of the sample, I extracted the data or that photo peak from the excel and fitted a Gaussian function to it using the curve fitting tool in matlab, like so.

Data Fit For Gaussian: I cherry picked the data for that peak from the raw data

From here I took the coefficient an set up the matlab code to produce just this Gaussian fit.

Code dataset = xlsread('Lab 3 Results 11.10.18 (1).xlsx','Sheet3','C394:D427');

x=dataset(:,1);

a1=38.51;

b1=1179;

c1=36.51;

y=a1*exp(-((x-b1)/c1).^2);

plot(x,y)

The part in green is not what I want and the part in read is, below is the code for what I belive is the total area or the read and green, i just not sure how to remove the green portion so I can get the data just for the red.

Code For numerical integration

dataset = xlsread('Lab 3 Results 11.10.18 (1).xlsx','Sheet3','C394:D427');

x=dataset(:,1);

a1=38.51;

b1=1179;

c1=36.51;

y=a1*exp(-((x-b1)/c1).^2);

int=trapz(y)

this code give int=$783.5391$ which is not far off the $529$ done by the cassy program, and my thought are that the my code is integrating the red and green area not just the red, but I am very new to matalb and not really sure what parameters are needed to get it to integrate just the red area.

Is there some advice someone could give

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