Answer
$$\frac{5\sqrt{5}-1}{2}$$
Work Step by Step
\begin{align*}
s&=\int_{a}^{b} \sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}} d t\\
&=\int_{0}^{1} \sqrt{9+36 t} d t\\
&= \frac{1}{36}\int_{0}^{1} 36\sqrt{9+36 t} d t\\
&=\frac{1}{36} \frac{2}{3}(9+36 t)^{3/2}\bigg|_{0}^{1}\\
&=\frac{5\sqrt{5}-1}{2}
\end{align*}
