A function \( I: \mathcal{C}[a, b] \rightarrow \mathbb{R} \) is a linear transformation if it satisfies the following two properties for all functions \( f, g \in \mathcal{C}[a, b] \) and all scalars \( c \in \mathbb{R} \):
1. Additivity: \( I(f + g) = I(f) +
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