Question

Would it be fair to explain to someone that an integral is adding together an infinite number of infinitesimally small things to make a real number?

Answer 1

Maybe you should instead make an analogy to particle physics, with things being made of molecules and molecules being made of atoms, etc. down to the quark level and further down to infinitesimally small things, but all together they sum to make something noticeable.

Answer 2

Why should I phrase it like that instead? I'm just asking if there's a fundamental flaw in my idea, or if it's genuine to what's actually going on.

Answer 3

see http://www.knowledgerush.com/kr/encyclopedia/Infinitesimal/
for a short discussion.