Find approximately, by using a calculator or other method to estimate the area,
$\int_0^1\,u^{2}\,\arcsin(u^{3})\,du \approx$

Then find the answer exactly, by applying the Fundamental Theorem of Calculus: if $F(u)$ is the antiderivative of $u^{2}\,\arcsin(u^{3})$ having no added constant, then
$$\int_0^1\,u^{2}\,\arcsin(u^{3})\,du = F(1) - F(0),$$ where
$F(1) =$
and
$F(0) =$ .