Relationship between integration with anti-derivative
An antiderivative is a differentiable function whose derivative is equal to (i.e., ).
Anti-derivative of a function is a function which on differentiation yields .
The process of solving for antiderivatives is called anti-differentiation, and its opposite operation is called differentiation, which is the process of finding a derivative.
Integration is connected with differentiation through the fundamental theorem of calculus: if is a continuous real-valued function defined on a closed interval then, once an antiderivative of is known, the definite integral of over that interval is given by.
The relationship between integration and anti-derivative is that integration of a function is equal to the sum of anti-derivative of the function and a constant (in case of indefinite integration) or it is the difference of the anti-derivative evaluated at the bounds of integration (in case of definite integration).