Find the length of the following two-dimensional curve.
[tex]
\mathbf{r}(t)=\left\langle 6 t^2-7,8 t^2+9\right\rangle, \text { for } 0 \leq t \leq 1
[/tex]
The [tex]\mathrm{arc}[/tex] length is [tex]\mathrm{L}\space =[/tex] (Type an exact answer, using radicals as needed.)