Answer
$\dfrac{\pi}{2}$
Work Step by Step
Since $ds=\sqrt {(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2} dt$
We have: $x= \cos \theta \implies \dfrac{dx}{dt}=-\sin \theta$
and $y= \sin \theta \implies \dfrac{dy}{dt}=\cos \theta$
So, $ds=\sqrt {(\cos \theta)^2+(-\sin \theta)^2} dt=dt$
We need to re-write the line integral in terms of $t$ to simplify the integral by using parametric equations.
Now, the line integral is:
$\int_C (x^2+y^2) ds=\int_0^{\pi/2} dt \\=[t]_0^{\pi/2}\\=\dfrac{\pi}{2}$
