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Answer by Ethan Bolker for Understanding the indefinite integral (without...

That's close enough to right for your stage of learning. There are a few subtleties that can come later.Doing integration first (which is where Archimedes started) you are setting yourself up for the...

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Understanding the indefinite integral (without reference to derivatives)

As I understand it, given some function $f$ integrable on $[a,b]$, we can define an indefinite integral of $f$ to be a function $F$ such that $$F(x)=\int_{n}^{x}f(t)dt,$$ where $n$ is some chosen fixed...

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