In the present theoretical work, the existence and uniqueness of a polynomial function of greater arc length that preserves the area under the curve of a given polynomial function of the same degree is shown. In this sense, it is intended to lay the foundations of its study starting from the most elementary situation: figures that are closed by a polynomial function and an interval in R^2. This with the idea that the determination of the curves that enclose this type of figures has a greater practical utility than the merely abstract study of the mapping between its superficial areas and serves as a source of problems of Mathematics at the university level.