Lebesgue Measures and Integrals : Let a,b be real numbers such that 0 < a < b < infinity. Does the limit [lim of ( integral from a to b of n*sin (x^2/n) dx], n is positive integer exist?

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  where lim is n as it approaches plus infinity (it is not specified so I believe the default when only n is listed is to plus infinity, I may be mistaken), *S* is my notation for the integral taken from a to b.

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