Arbitrary constant of integration

The constant of integration, mostly referred to as \(C\), is always in the result of an indefinite integration. This mainly arises because of the fact that once you take the derivative of a constant, you'll always get 0. So when you take the derivative of a function with a constant term, that term vanishes and has no impact on the solution. This leads us to the conclusion that when you take the anti-derivative of something, you must add the constant of integration because there are an innumerably infinite number of possible solutions with all sorts of constants, and all give the same derivative.