Countour integral $\int {{{(\overline z )}^2}dz} $ > Evaluate $\int {{{(\overline z )}^2}dz} $ along the straight line segment from $z=0$ to $z=2+i$. My attempt to this question is I change z into $x+iy$ and do the integration; $$\int_0^{2 + jy} {(x -yi)(x -yi)} dz$$ So, my question is how to do integration with respect to z?

Note that: $$z=0\to2+i\implies z(t)=(2+i)t\quad t\in[0,1],t\in\mathbb R\\\\\int\bar z^2dz=\int_0^1 \overline{(2+i)}^2t^2(2+i)dt=(2-i)^2(2+i)/3=5(2-i)/3=10/3-5i/3$$