We say $f(z)$ is regular in $D$ if for every point $z\in D$, $f$ is differentiable.
The question comes with regards to Cauchy formula and Newton-Leibniz formula for
$$\int_\gamma \frac{1}{4z+iz^2}\mbox{d}z $$
where $\gamma$ is the boundary of a triangle with vertices $-i, 2+i,-2+i$.
Applying the actual formulae is not the problem. However, both Cauchy and N-L are applicable if $f$ is regular in $D$. Clearly, there is a singularity in the triangle at $0$. Can $f$ be regular in $D$ (the triangle), regardless?
Can we still apply these formulae, am I overlooking something?
What about N-L case?