I'm just starting to learn about anti-derivative (which is basically function F whose derivative is equal to the original function f).

What I want to know is that, is anti-derivative and integral the same thing?

And if so, what is a definite integral? My textbook doesn't go into definite integrals, right know we are dealing with indefinite integrals. What does this mean?

Please don't get too mathy in the explanation

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    $\begingroup$ indefinite integral is antiderivative, definite integral is area under curve. $\endgroup$ – Karolis Juodelė Dec 2 '16 at 20:43

The indefinite integral is the set of antiderivatives (hence the important $+C$ for intervals) and the definite integral is accumulation - equal to the area under the curve $y=f(x)$ if $f \geq 0$. Bottom line:

antiderivative --- one function

indefinite integral --- set of functions

definite integral --- number.

As mentioned in a comment, antiderivatives and definite integrals are related by (a version of) the Fundamental Theorem of Calculus.

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    $\begingroup$ I think it would be nice to show their relationships between definite and indefinite. ;) $\endgroup$ – Simply Beautiful Art Dec 2 '16 at 20:52

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