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Integrating form over a path on projective algebraic curve

Let $X$ be an algebraic projective curve in $\mathbb{C}P^2$ given by $$ X = \left\{ w \in \mathbb{C}P^2 \mid w_0^2 = w_1 w_2 \right\}. $$ I have a differential form on $X$ defined by $$ ...