How did Newton develop calculus and why use antiderivatives?

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eddybob123
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when isaac Newton was inventing calculus, how did he do it? why do we get the antiderivative? why do we have to F(b)-F(a)? I am just interested to know.
 
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I really have no clue what you are asking. Have you taken a Calculus course? Why we would want to find an anti-derivative and why we subtract the values of the anti-derivative at two different points are explained in any Calculus text.

And they have nothing to do with how Newton (and Leibniz) developed Calculus to begin with.
 
Did you just find that theorem in a book somewhere?