Question: Suppose I is continuous on [0, 1]. Must there be a nondegenerate closed subinterval [a, b] of [0, 1] for which file restriction of I

Suppose I is continuous on [0, 1]. Must there be a nondegenerate closed subinterval [a, b] of [0, 1] for which file restriction of I to [a, b] is of bounded variation?

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