"We are given:"
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ F(x) = int_0^x \ sqrt{ t^3 + 1 } \ dt.
"So, directly by a Fundamental Theorem of Calculus, we have"
"at once:"
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ F'(x) = sqrt{ x^3 + 1 }.
"Thus:"
\qquad \qquad \qquad \qquad \qquad \qquad F'(2) = sqrt{ 2^3 + 1 } = sqrt{ 9 } = 3.
"So:"
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad F'(2) = 3.