Using the concepts of derivative and integral of fuzzy functions in the sense of fuzzification, this paper is devoted to studying a new version fuzzy fundamental theorem of calculus as well as a new variant of fuzzy Taylor formula with an integral remainder in the univariate and multivariate cases. Here, the fuzzification of derivative and integral means using Zadeh \'s extension principle on the corresponding classical operators. Indeed, by presenting appropriating symbols, it is shown in this work, contrary to what was supposed to be, Zadeh \'s extension principle is capable of making the ability to compute and introduce many quantities and concepts in univariate and multivariate calculus such as integral, derivative, Taylor expansion and etc.

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