hi here is the question, by integrating explicitly in the complex plane, evaluate

where C is the half-circle centered at z = 1 with radius 1, starting at z_0 = 2 and ending at z_1=0, and traveresed in the upper half-plane. Show that the fundamental theorem of calculus holds for this example.

here's my working out:

parametrise:

let and

my fundamental part doesnt equal, coz when i did it i got -128/7

so can someone please help me where i got it wrong?

coz when i FIRST did it i parametrise this way:

then

and i got the same answer as the fundamental part, but since the question says centered at z = 1 dont you have to add the 1 to z(t)?