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The definite integral of a function computes the area under the graph of its curve, allowing us to calculate areas and volumes that are not easily done using geometry alone.

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If \(\displaystyle f(x) = \int_{x}^{x+1} (2t^2+t)\ dt\), what is the value of \(f'(7)\)?

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Is the above statement true?

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Given function \[g(x)=\int_{0}^{x} \sqrt{1+t^{3}}dt,\] what is \(g'(x)?\)

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