I have the line integral

\int y sin(x) i -cos(x) j

Over (0,1) (pi,-1) and I want to make the integral a function of a single value t.

Can someone please check my Parameterization

I'm using the Parameterization

r(t) = (1-t)(x0,y0) + t(x1,y1)

= (1-t)(0,1)+t(pi,-1)

= pi t 1-2t

so
x = pi t therefore x'(t) = pi

y = 1-2t therefore y'(t) = -2

regards