Step 1: Analyze the reaction.
The reaction involves the oxidation of \(I_2\) to \(ICl\) and reduction of \(KClO_3\) to \(KIO_3\). Here, iodine (I) is oxidized and chlorine (Cl) is reduced.
Step 2: Identify oxidation numbers.
- The oxidation number of iodine in \(I_2\) is 0, and in \(ICl\), it is +1. Therefore, iodine undergoes an increase in oxidation state by 1 (from 0 to +1).
- Chlorine in \(KClO_3\) has an oxidation state of +5, and in \(KIO_3\), it remains +5.
Step 3: Analyze the statements.
- Option \((1)\): \(I_2\) acts as an oxidizing agent because it is reduced to \(ICl\), so this statement is correct.
- Option \((2)\): \(KClO_3\) acts as an oxidizing agent, not as a reducing agent, so this is incorrect.
- Option \((3)\): Chlorine does not undergo a change in oxidation number, so this statement is incorrect.
- Option \((4)\): The oxidation number of iodine increases by 2, from 0 in \(I_2\) to +1 in \(ICl\).
Step 4: Final Answer.
Thus, the correct statement is \(I\) increases in oxidation state by 2, corresponding to option \((4)\).