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Thus the operation $d/d\mathbb{I}$ was mapping the integral \begin{equation}  \frac{d/d\mathbb{I}}\int_a^b \frac{d}{d\mathbb{I}}\int_a^b  f(x) dx \to \int_a^b xf'(x) dx \end{equation}  and the answer \begin{equation}  \frac{d/d\mathbb{I}}I \frac{d}{d\mathbb{I}}I  \to -I + [xf(x)]_a^b \end{equation}