Question

"if f(x) be any one integral of f(x), then f(x)+c is its general integral."

Answer 1

Constant of integration

In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) on a connected domain is only defined up to an additive constant, the constant of integration.[1][2] This constant expresses an ambiguity inherent in the construction of antiderivatives. If a function {\displaystyle f(x)} is defined on an interval and {\displaystyle F(x)} is an antiderivative of {\displaystyle f(x)}, then the set of allantiderivatives of {\displaystyle f(x)} is given by the functions {\displaystyle F(x)+C}, where C is an arbitrary constant (meaning that any value for C makes {\displaystyle F(x)+C} a valid antiderivative). The constant of integration is sometimes omitted in lists of integrals for simplicity