This functional is inner product with $g=1_{[0,2]}-1_{[3,10]}$. Cauchy–Schwarz gives $|T(f)|\leq\|f\|_2\|g\|_2$, and equality is attained by a scalar multiple of g. Thus $\|T\|=\|g\|_2=\sqrt{2+7}=3$. The gap (2,3) contributes zero.
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