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The curve is a semicircle with radius 1 -- it's length is $\pi$. You can use the arc-length formula to get this

$$\int_0^\pi \sqrt{cos(t)^2+sin(t)^2} dt = \int_0^\pi 1 dt = \pi$$ .

Finally, in Sage:

sage: parametric_plot((cos(x), sin(x)), (x, 0, pi))
sage: integrate(sqrt(cos(x)^2+sin(x)^2),x, 0, pi)
pi