Does anyone know, where I can find the proof of necessary and sufficient conditions for differentiating under the integral sign in case of Henstock integral? Here are the theorems but not all the proofs:

Necessary and sufficient conditions for differentiating under the integral sign
Erik Talvila
arXiv:math/0101012

We give necessary and sufficient conditions for differentiating under the integral sign an integral that depends on a parameter. The conditions require the equality of two iterated integrals and depend on being able to integrate every derivative. The Henstock integral is thus used in an essential way.