Glaisher, J. W. L., ed. (1894). "Biographical sketch". The Collected Mathematical Works of Henry John Stephen Smith. Oxford Clarendon Press. Retrieved 27 November 2012.
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The Riemann integral was introduced in Bernhard Riemann's paper "Über die Darstellbarkeit einer Function durch eine trigonometrische Reihe" (On the representability of a function by a trigonometric series), submitted to the University of Göttingen in 1854 as Riemann's Habilitationsschrift (qualification to become an instructor). It was published in 1868 in Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen (Proceedings of the Royal Philosophical Society at Göttingen), vol. 13, pages 87–132 (freely available on-line from Google Bookshere): Riemann's definition of the integral is given in section 4, "Über der Begriff eines bestimmten Integrals und den Umfang seiner Gültigkeit" (On the concept of a definite integral and the extent of its validity), pp. 101–103, and Smith (1875, p. 140) analyzes this paper. Smith, H. J. S. (1875), "On the integration of discontinuous functions", Proceedings of the London Mathematical Society, 6: 140–153, JFM07.0247.01.
The Riemann integral was introduced in Bernhard Riemann's paper "Über die Darstellbarkeit einer Function durch eine trigonometrische Reihe" (On the representability of a function by a trigonometric series), submitted to the University of Göttingen in 1854 as Riemann's Habilitationsschrift (qualification to become an instructor). It was published in 1868 in Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen (Proceedings of the Royal Philosophical Society at Göttingen), vol. 13, pages 87–132 (freely available on-line from Google Bookshere): Riemann's definition of the integral is given in section 4, "Über der Begriff eines bestimmten Integrals und den Umfang seiner Gültigkeit" (On the concept of a definite integral and the extent of its validity), pp. 101–103, and Smith (1875, p. 140) analyzes this paper. Smith, H. J. S. (1875), "On the integration of discontinuous functions", Proceedings of the London Mathematical Society, 6: 140–153, JFM07.0247.01.
The Riemann integral was introduced in Bernhard Riemann's paper "Über die Darstellbarkeit einer Function durch eine trigonometrische Reihe" (On the representability of a function by a trigonometric series), submitted to the University of Göttingen in 1854 as Riemann's Habilitationsschrift (qualification to become an instructor). It was published in 1868 in Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen (Proceedings of the Royal Philosophical Society at Göttingen), vol. 13, pages 87–132 (freely available on-line from Google Bookshere): Riemann's definition of the integral is given in section 4, "Über der Begriff eines bestimmten Integrals und den Umfang seiner Gültigkeit" (On the concept of a definite integral and the extent of its validity), pp. 101–103, and Smith (1875, p. 140) analyzes this paper. Smith, H. J. S. (1875), "On the integration of discontinuous functions", Proceedings of the London Mathematical Society, 6: 140–153, JFM07.0247.01.