Abstract
In the current curriculum, The result of the fundamental theorem of calculus, F(b)-F(a) is presented as the definition of definite integral. This definition of definite integral was proposed by Lacroix in the lately 18th century and was used in various calculus textbooks in the first half of the 20th century. In this study, I analyzed the relationship between the differential and the integral calculus, searched the mathematical meaning of the definition of the Lcaroix-style definition of the definite integral, and surveyed the integral calculus chapters of calculus textbooks that adopted such definition. Based on these discussions, I proposed some suggestions to improve the teaching of the integral calculus.
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