Indefinite integration, also known as anti-differentiation, is the reversing of the process of differentiation. Instead of having a set of boundary values, one only finds an equation that would produce the integral due to differentiation without having to use the values to get a definite answer. The indefinite integral represents a family of functions whose derivatives are f. The difference between any two functions in the family is a constant. Using the Integral Key. Finding an anti-derivative is an important process in calculus. It is used as a method to obtain the area under a curve and to obtain many physical and electrical equations that scientists and engineers use every day.