Line integral, half circle, polar coordinate the only way

Question

In solving Line Integrals, C is the upper half of x^2+y^2=1 from (1,0) to (-1, 0).

do we have to set,

x=cos(t), y=sin(t)
dx=-sin(t), dy=cos(t)
0<t<pi

or can we use the start/end points and use a line segment.

r(t)=(1-t)r0 + tr1
    =(1-t)<1,0> + t<-1,0>
    =<1-t, 0> + <-t1,0>
    =<1-2t, 0>
r'(t) = <-2, 0> 
0<t<1

Even though the line moves along the circle axis, since we have the start and end point, can't we just use the line segment method? instead of polar coordinates?