  In calculus, an indefinite integral of a function $f$ is a differentiable
function $F$ whose derivative is equal to $f$. In present paper, we generalize
this notion of the indefinite integral from the ring of real functions to any
ring. The main goal of the paper is to focus on the properties of such
generalized integrals that are inherited from the well-known basic properties
of indefinite integrals of real functions.
