Contour integral $\int_c {(z - {i^2})dz} $ over the line segment from $0$ to $1+2i$

Question

Hello can someone help me to solve this problem?

Evaluate the integral where $c$ is the straight line segment joining $0$ and $1+2i$.

$$\int\limits_c {(z - {i^2})dz} $$

Answer 1

Parametrize $z=t(1+2i)$ to get $$ \int_c(z-i^2)\,\mathrm{d}z=\int_0^1\overbrace{(t(1+2i)+1)}^{(z-i^2)}\overbrace{(1+2i)\,\mathrm{d}t}^{\mathrm{d}z} $$