The curve is a semicircle with radius 1 -- it's length is $\pi$. You can use the arc-length formula to get this
$$\int_0^\pi \sqrt{cos(t)^2+sin(t)^2} dt = \int_0^\pi 1 dt = \pi$$.
sage: parametric_plot((cos(x), sin(x)), (x, 0, pi))