Book Calculus by Thomas/Finney, 9th Edition, Page 275
Differential Calculus to Integral Calculus. This is where we stop asking “how fast is it changing?” and start asking “how much have we accumulated?”
Indefinite Integrals
The chapter kicks off with a simple question: If I give you the answer (the derivative), can you tell me the original question (the function)?
This is the concept of the Antiderivative. If we know the rate of change is $f'(x)$, we want to find $f(x)$. However, there is a catch. Since the derivative of a constant is zero, we can never be 100% sure what the original constant was. This gives us the “family of functions” known as the Indefinite Integral, represented by that famous $+C$:
$\int f(x) \, dx=F(x) + C $
Example.
