The characteristics of a function are usually investigated by looking at the continuity of the function. But what happens if a function does not have continuous properties? To what extent can the characteristics of continuous function be maintained for discontinuous cases? The stochastic function that is widely involved in solving problems in the field of average financial mathematics is a discontinuous function. This is reflected by the acquisition of a smooth curve from the modeling drawing

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... tained. Today, the nature of continuous functions in [a, b] has been widely studied and developed. Some properties of the continuous function can be extended to the appropriate discontinuous function. In this paper, there will be some integral reviews for discontinuous functions which are closely related to stochastic functions.