Integrating n-unisolvent sets of functions

We prove that integrating an n-unisolvent set F of continuous real-valued functions on some open or half-open interval of ℝ gives an (n + 1)-unisolvent set S(F) of functions. If F solves the Hermite interpolation problem and the interval is open, then 5(F) also solves the Hermite interpolation problem. In a second section we verify to what extent these results can be generalized to n-unisolvent sets of analytic functions defined on domains in ℂ. The n-unisolvent sets in this section are linear spans of Chebyshev systems that are associated with completely (n - 1)-valent functions.