[jamesmaniscalco]

They're not totally separate concepts though, no? The definite integral is the difference of two values of the indefinite integral (antiderivative).

I suppose if you're talking about solving them computationally, you can calculate/approximate the definite integral by taking the limit of the sum as you reduce the step size, whereas performing the indefinite integral requires a different method (chain rule etc.). But when doing them by hand usually the first step in calculating a definite integral is finding the antiderivative.

[globular-toast]

That's the thing. What tends to stick in people's heads is the bit that hurts. You can tell someone that integration is "just a continuous sum" and you might see a ligthbulb go on. But then the bad news: you still need to find this magical function F(x) and to do that requires intuition and guesswork. Understanding it's "just a sum" doesn't help at all with finding the antiderivative.

[Chris2048]

> Understanding it's "just a sum" doesn't help at all with finding the antiderivative

No, but you can still integrate computationally (difference method).