>>42582739The addition sign represents the sum of two discrete numbers. The sigma represents the discrete sum of a function, and the long S represents the total change in a system, the system being represented by a continuous function. The long S is actually reducible to the sigma in conjunction with the concept of limit. The limit definition of integration (long S) is usually taught before antiderivatives, but historically limits came later after Gottfried Leibniz, the inventor of the long S notation, had died.
