How to integrate discrete data by Gaussian quadrature method

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Hello,
I'm trying to numerically integrate discrete data by Gaussian quadrature method. The file attached "test.mat" is a discrete data set taken from a finite-element mode solver and has the following variables.
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x, y : Coordinates of each node
nodes : Node of each triangular element
normE : Electric field distribution
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How can I apply Gaussian quadrature method to the data set attached to calculate the area integration below?

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José-Luis
José-Luis 2016-6-29

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