How to Integrate Artifical Neural Networks

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How can one calculate the integral of a neural network? Is there a better method than writing the output as a function of the input then trying usual integration methods?

Even a (sufficiently good) approximation can suffice in my case, where I am trying to fit complicated high dimensional data sets to neural networks and curve fitting them with it, and I would like to add an integration/differentiation feature.

Should I just use usual methods for numerical integration like Gauss-Legendre or is there something I'm missing?