The Ito integral is a mathematical concept used in stochastic calculus, which deals with integrating functions with respect to stochastic processes, particularly Brownian motion. Unlike traditional integrals, the Ito integral accounts for the randomness in these processes, making it essential for modeling phenomena in finance and other fields. Developed by Japanese mathematician Kiyoshi Ito, this integral allows for the analysis of systems influenced by random fluctuations. It plays a crucial role in the formulation of the Ito's lemma, which is a fundamental result in stochastic calculus, helping to derive the dynamics of various stochastic models.