That's not correct. However it would be correct if f(x, t) fulfill certain criteria. Consider following example where variable y is variable tpic.twitter.com/7K9Yj6Aopb
When a,b are constants, we can pull the total derivative inside the integral as a partial derivativepic.twitter.com/s8Kwvmd7Bp
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Indeed there are the usual non-pathological conditions on f
End of conversation
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