Show that \( f: [a,b] \to \mathbb R \) is Riemann integrable on \([a,b]\) if and only if there exists \( L \in \mathbb R \) such that for every \( \epsilon > 0\) there exists \( \delta_{\epsilon} > 0 \) such that if \(\mathcal P \) is any tagged partition with norm \( ||\dot{\mathcal P} || \leq \delta_\epsilon \), then \( | S ( f; \dot{\mathcal P}) - L | \leq \epsilon \).

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