Primitives of continuous functions via polynomials

TL;DR

This paper provides an elementary proof, using Bernstein polynomials, demonstrating that every continuous function on the unit interval has a primitive function, emphasizing a classical approach in analysis.

Contribution

It offers a self-contained, folkloristic proof of the existence of primitives for continuous functions using limits of Bernstein polynomial primitives.

Findings

Proof confirms existence of primitives for continuous functions

Uses limits of Bernstein polynomial primitives

Provides an elementary, self-contained approach

Abstract

We present an elementary self-contained folkloristic proof, using limits of primitives of Bernstein polynomials, for the existence of primitive functions of continuous functions defined on the unit interval.