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in this video were going to talk about the first part of the fundamental theorem of calculus so if g of x is equal to the definite integral of f of t from a to x then g prime of x is going to equal f of x so if g is the antiderivative of f then the derivative of g will equal f the derivative of the antiderivative will give you the original function another way in which you can express the second part of the i mean the first part of the fundamental theorem of calculus is you can express it this way the derivative of the integral from a to x of f of t dt is going to equal f of x and for the most part youre replacing t with x but thats not always the case as some examples will illustrate but thats the basic idea behind the first part of the fundamental theorem of calculus some textbooks may call it the second part of the fundamental theorem of calculus but regardless of what they call it the principle still remains the same now lets work on an example problem so lets find the deriva
