Problem $3($Arc length of parameterized curve$).$ Compute the arc length of the parameterized curve:

$x(t)=\frac{4}{3}{t}^3+t-2$

$y(t)=\frac{1}{27}(9t^2+2{)}^{\frac{3}{2}}$

for $0t1.($Don$\text{'}$t forget to use the chain rule!$)$