#### Answer

$$\dfrac{7}{3}$$

#### Work Step by Step

We calculate the line integral by using substitution as follows:
$$ ds=\sqrt {(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2+(\dfrac{dz}{dt})^2} dt\\ =\sqrt {t^2} dt \\= t \space dt $$
$$\int_C f(x,y) ds=\int_{0}^{\sqrt 3} \sqrt {(1+t^2)} t \space dt \\= (\dfrac{1}{3})[(1+t^2)^{3/2}]_{0}^{\sqrt 3} \\=\dfrac{7}{3}$$