Note 1 — THE INTEGRATION OF FUNCTIONS OF A SINGLE VARIABLE I. Introduction

Euler, the first systematic writer on the 'integral calculus', defined it in a manner which identifies it with the theory of differential equations: 'calculus integralis est methodus, ex data differentialium relatione inveniendi relationem ipsarum quantitatum' (Institutiones calculi integralis, p. 1). We are concerned only with the special equation (1), but all the remarks we have made may be generalised so as to apply to the wider theory.