Answer
$\oint_C ds=\oint_C dx=\oint_C dy=0$
Work Step by Step
For a vector field to be Conservative, $\dfrac{\partial f_1}{\partial y}=\dfrac{\partial f_2}{\partial x}$
Also, the curve is $r(t)= ( \cos t, \sin t)$
In order to compute the $\oint_C ds$, we have the force field $f(x,y)=(1,1)$
This gives: $\dfrac{\partial f_1}{\partial y}=0=\dfrac{\partial f_2}{\partial x}$. This means that $\oint_C ds=0$
Similarly, by the doing the same above calculations, we find that
$\oint_C ds=\oint_C dx=\oint_C dy=0$
