I've just encountered this somewhere and I need some sort of formal proof for why a continuous function ##f(x)## can equal zero because its integral is zero. Are there any out there? I've seen similar forum posts on places like Stack Exchange and one here, but I can't exactly follow the logic they always use in their proof. Can anyone point me to a full/formal proof and/or explain how it is that others arrive at their proof? Thanks for any help!