Remember summation from elementary school. Usually, when you sum something. , you do it with discrete values. Seemingly easy, but not well understood since applications of these arithmetic only help in everyday-life when using countable values: like money, apples or the world-famous watermelons. Since many text-book examples are quite out of touch with reality and most curricula soon after that focus on solving equations, the concept of functions themselves seldom pops up during middle-school education.

Integration is generalized summation of continuous functions, but since functions are only seldom done in middle-school, it is kind of hard to dive more deep into this topic.

Facts are:

• almost all mathematical operations itself are functions
• integration has weak requirements to be applicable on some function
• you need at least some knowledge about sets to be able to comprehend, why integration is mightier than differentiation.

So: From my personal pov, it is taught the wrong way around. But I also am able to admit, that not every student is eligible to look at this, like it "really" is.

My school-days are mostly done, but i know from firsthand that there are people out there, being able to comprehend concepts "way-beyond" understanding.

Like summation over dimensions or tensors itself, which explain most.

Integration only needs weak assumptions (from a mathematical-pov) to be to put to actual useful purposes.

While number-theory itself, the same as "standard"-algebra, needs a lot of them, especially, when questioned.

I just wish, I learned about integration a lot earlier. That's it.