Solution
= Solution
<Morera's theorem> says that a <continuous> complex-valued <function> $f$ on an <open set> $U\subseteq\mathbb C$ is <holomorphic> if
$$
\boxed{\int_{\partial T}f(z)\,dz=0}
$$
for every triangle $T$ whose closed interior is contained in $U$. Triangle boundaries are traversed with positive orientation. The <continuity> hypothesis matters: the zero-integral condition is combined with <continuity>, not used in isolation.