A function f(x)f(x)f(x) is defined by the integral f(x)=∫0x2t3+1 dtf(x) = \int_{0}^{x^2} \sqrt{t^3 + 1} \, dtf(x)=∫0x2t3+1dt. What is the value of f′(1)f'(1)f′(1)?
222\sqrt{2}22
2\sqrt{2}2
23\frac{2}{3}32
111