What constant must be added to an indefinite integral?

In the context of indefinite integrals, it is essential to include a constant because the process of integration is essentially the reverse of differentiation. When you differentiate a constant, it disappears since the derivative of any constant is zero. Consequently, when you perform integration, you must account for the possibility of any constant that may have been there before differentiation took place.

The constant typically added to an indefinite integral is often denoted as 'C'. This 'C' represents all possible constant values that could be resulting from the integration process; without it, the integral would only represent a particular antiderivative rather than the entire family of antiderivatives that differ by a constant.

Including this constant ensures that the indefinite integral captures all potential functions that could lead to the original differentiated expression, enhancing the generality and completeness of the solution. Hence, the correct addition of a constant to the indefinite integral is denoted by 'C', encapsulating the necessary arbitrariness due to the nature of differentiation.