We are doing something simiar to this but with real numbers so im thinking it should work. If not im sorry.
After you reparamertize the funcion you need to differeniate with respect to t:
x = t
y = 1 - t
I dont believe you do this implicitly...
dx/dt = 1
dy/dt = -1
Now your equation is a function of time and it should be (i think) integrated from -1 to 1.
Also your need to up in "t" everyhwere in there was a "z" before in the equation. This is because the function should be changed from "F(z)=" to "F(z(t))=", assuming your first function was "f".