(Solution) - Another way to write the Fundamental Theorem of Calculus sometimes -(2025 Original AI-Free Solution)

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Another way to write the Fundamental Theorem of Calculus (sometimes called the First Fundamental Theorem of Calculus) relates the definite integral and the derivative. It states that if we treat the definite integral ?xa f(s)ds as a function of x, then

for any value of a. Check this in the following cases by computing the definite integral and then taking its derivative.
f(x) = 1 + x3 with a = 1.