Check solution of integral

I'm preparing for an exam and would like someone to check this if possible

$\displaystyle \int_{C}(z^{2}+z)dz $ where $\displaystyle C $ is any path from $\displaystyle -i $ to $\displaystyle 2+i $

I figured out that $\displaystyle (z^{2}+z) $ was not analytic using cauchy riemann equations

So i parametrized $\displaystyle -i $ to $\displaystyle 2+i $ using the formula

$\displaystyle z(t) = a + (b-a)t $ where $\displaystyle 0<=t<=1 $

Filling into the above formula i got $\displaystyle z(t) = 2t + i(t-1) $

and $\displaystyle \frac{dz}{dt} = 2+i $

So i said $\displaystyle \int_{C}(z^{2}+z)dz = \int^{1}_{0}[(2t + i(t-1))^{2} + (2t +i(t-1))](2+i)dt $

i proceed to work this out an got an answer of $\displaystyle -\frac{5}{3} - \frac{4}{3}i $

The answer isn't really that important to me, i just would like to know if the line above my answer is correct

Thanks,

Piglet