I've been trying to solve it since 3-4 days, and I can't seem to find a way to solve it. If someone could, I'd feel so much appreciated

\(\text{You've got an open contour that's already parameterized for you, so just plug stuff in}\\ \displaystyle \int_C z^2+\bar{z}~dz,~C = 1+i t,~t \in [0,2]\\ \displaystyle \int_0^2~(1+it)^2+(1-it)~dt\\ \text{If you're doing contour integrals in the complex plane then you can do that integral}\)