How to Integrate a double derivative of a discrete Function

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L&G, I desperately need your help:
g(x,y) is an n by m matrix representing an image.
I am trying to calculate the below f function
f(x,y) = integral of {d2 g(x,t)/dx2}.dt between y and Ymax
d2 being the double derivative
Thank you in advance for your help ...!

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