An indefinite integral is a fundamental concept in calculus that represents the collection of all antiderivatives of a given function. It is denoted by the integral sign ∫ followed by the function and the differential variable, such as ∫f(x)dx. The result of an indefinite integral includes a constant of integration, usually represented as +C, because there are infinitely many antiderivatives differing by a constant. Indefinite integrals are essential for solving problems related to areas under curves, rates of change, and various applications in physics and engineering. They are closely related to the concept of differentiation, where the process of finding an indefinite integral essentially reverses differentiation, allowing us to recover the original function from its derivative.