Complex Contour Integrals Answer check

Question

can someone check my answers for the following question:

Evaluate the integrals $\ \int{z^2 dz} $ and $\ \int{|z|^2} dz $ along the following paths

a) line from 1 to i

b) quarter of the unit circle from 1 to i

Answers:

a) z^2 : -1 - i

 |z|^2 : -2/3 +2/3 i

a) z^2 : -1/4 + 1/4 i

 |z|^2 : -1 + i

Answer 1

Without knowing the actual answers, I know that your answers for $\int z^2 \, \mathrm{d}z$ can't be right because $z^2$ is holomorphic and hence the integral does not depend on the path (Cauchy's integral theorem).