Problem 1485 (difficulty: 5/10)

Give a sequence \(\displaystyle f_n:[0,1]\to\R\) that converges pointwise, for which \(\displaystyle \lim\int_0^1f_n\) exists but \(\displaystyle \lim\int_0^1f_n\ne\int_0^1\lim f_n\).

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