Indefinite integrals, also known as antiderivatives, represent a family of functions whose derivative is the original function. They are denoted by the integral sign ∫ followed by the function and the differential variable, such as ∫f(x)dx. The result includes a constant of integration, usually represented as +C, because differentiating a constant yields zero. Indefinite integrals are fundamental in calculus and are used to solve problems involving area under curves, motion, and accumulation. Techniques for finding them include substitution and integration by parts, which are essential tools in the study of calculus and mathematics.