Let $\gamma : [0,1] \to \mathbb{C}$ be a $C^1$ curve with $\gamma(0) = i, \gamma(1) = -i$ such that $\gamma$ does not intersect $(-\infty,0] $.
Calculate the integral
$$ \int_{\gamma}^{} \operatorname{Log}^2(z) \,dz\ $$
I have applied the definition of integration of a complex valued function on a path as so: $$ \int_{\gamma}^{} \operatorname{Log}^2(z) \,dz\ = \int_{0}^{1} \operatorname{Log}^2(\gamma(t))\gamma'(t) \,dt\ $$
The question says to use the fundamental theorem of calculus but I can't find a primitive/antiderivative for this.