Integrating completely unisolvent functions (Q1899370)

\(f:\mathbb{R}^n\times I\to\mathbb{R}\) is a continuous function and \(\text{INT}(f)\) is the set of all functions \(x\mapsto f(a_1, \dots, a_n,x)\) from \(\mathbb{R}\) to \(\mathbb{R}\). A function \(g\in \text{INT} (f)\) interpolates \(m\) points \((x_i,y_i)\in I\times R\), \(i=1,2, \dots,m\) if \(g(x_i)=y_i\) for all \(i\). The function \(f\) is \(n\)-unisolvent if for any choice of points \((x_i,y_i)\in I\times R\), \(i=1,2, \dots,n\), \(x_1<x_2< \cdots <x_n\), there exists a uniquely determined \(g\in\text{INT}(f)\) that interpolates all \(n\) points. In this paper, the author shows that the integral of a completely \(n\)-unisolvent function defined on an interval is a completely \((n+1)\)-unisolvent function.