What is “+C”?
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We use the constant of integration (+C) to account for any constants that may have been "derived" out of the original function.
An indefinite integral is an integral without bounds.
A.k.a... what we've been working with so far! We'll get to definite integrals soon.
Scenario: Given f(x) and f'(x), take the integral of f'(x) to return to f(x).
This works because f(x) didn't have a constant in it!
Scenario: Given g(x) and g'(x), take the integral of g'(x) to return to g(x).
The +1 gets "derived" out of g'(x)...
...so when we try to take the integral of g'(x) to get it back to g(x)... it's missing the +1!
Include "+C" whenever taking integrals to account for constants that may have been "derived" out!
We need an initial condition of the integrated function, a.k.a. a point on it that we know exists!