I don't know if I can plug-in here some of the materials I prepared some years ago. It might help to bridge/connect the use of Monte Carlo techniques and its relations with integration:
Also just to mention something else that is very interesting related with MC : "quasi-Monte Carlo techniques" (small example in https://github.com/ChristopheRappold/MCandPython/blob/master... ). For people interested in MC, just take a look to those keywords.