Integration or anti differentiation is the process of finding a function given the derivative is already known. It essentially is and can be thought of as finding the derivative in reverse.
If we assume that:
Then we can write the integral of f(x) as:
Where C is an arbitrary constant that defines the function F(x) which cannot be calculated from the function f(x)
The definite integral can be calculated as
Here we can see that if we left in the arbitrary constant for the definite integral it would cancel out as we minused F(a) from F(b).
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