Quick question

im trying to calculate the integral around the closed curve C of

z(bar) dz where z(bar) is the complex conjugate of z

where C is the unit circle.

Using the subsitution z = e^it i calculated the integral to be 0.

=> z(bar) = e^-it

However after finding the question in a maths book the answer is given to be 2pi(i).

Can any of ye tell me which solution is correct