Discussion
The derivative \( \dfrac{d}{dx}\displaystyle\int_{0}^{x} f(t)\,dt \) equals
Answer: D
This is the first form of the fundamental theorem: the integral accumulates the function, and differentiating recovers it,
\[ \frac{d}{dx}\int_{0}^{x} f(t)\,dt \;=\; f(x). \]
It is the statement that integration and differentiation are inverse operations, and it is why the accumulated area is an antiderivative for any continuous integrand
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