We prove that the only functions for which certain standard numerical integration formulas are exact are polynomials.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am31-1-1, author = {Pawe\l\ Szeptycki}, title = {Integration of polynomials}, journal = {Applicationes Mathematicae}, volume = {31}, year = {2004}, pages = {1-4}, zbl = {1072.41017}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-1-1} }
Paweł Szeptycki. Integration of polynomials. Applicationes Mathematicae, Tome 31 (2004) pp. 1-4. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-1-1/