Does anyone know of a good undergraduate or graduate text that gives a brief rundown of the Riemann integral on Banach space valued functions?
This one might be what you are looking for:
MR2419362 (2009e:00001) Amann, Herbert ; Escher, Joachim . Analysis. II. Translated from the 1999 German original by Silvio Levy and Matthew Cargo. Birkhäuser Verlag, Basel, 2008. xii+400 pp. ISBN: 978-3-7643-7472-3; 3-7643-7472-3
I also think there should be something in Henri Cartan's book on Differentiable Calculus.