Condition for Darboux Integrability/Historical Note

Historical Note on Condition for Darboux Integrability
The necessary and sufficient conditions for the existence of a Riemann integral were determined by in his paper  of $1854$, on the subject of Fourier series.

It is noted that the proof given on this page refers specifically to the Darboux integral, which is a simpler but equivalent concept to that introduced by.

That they are equivalent is given in Equivalence of Definitions of Riemann and Darboux Integrals