Given that $\displaystyle 1 \le \sqrt{x^3+1} \le 3$ on [0, 2] to estimate $\displaystyle \int_{0}^{\,2} {\sqrt{x^3+1}}\, dx\,.$

$\displaystyle \le \int_{0}^{\,2} {\sqrt{x^3+1}}\, dx \le$