This is the second edition of Isaac Todhunter’s Treatise on the Integral Calculus, containing a host of improvements, corrections and additions over its predecessor. In this work, Todhunter presents the nascent field of calculus as it existed in the 19th century. The publication covers the basic concepts necessary for mastering the subject, including determinants, series and power series; along with an extensive appendix of applications dealing with analytic geometry, differential equations and mechanics.