Verified answer

Since z = x + iy, this equals

∫c (x - iy) * (dx + i dy)

= ∫(x = 0 to 3) (x - ix^2) * (1 + i * 2x) dx, since y = x^2

= ∫(x = 0 to 3) (x + ix^2 + 2x^3) dx

= (x^2/2 + ix^3/3 + x^4/2) {for x = 0 to 3}

= 45 + 9i.

I hope this helps!