Question

\[\frac{d}{dx} \int_a^bf(x)dt=\int_a^b\frac{df(x)}{dx}dt\]
Why is the equality correct?

Answer 1

http://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign
It's to do with this, but the article didn't help me much

Answer 2

did you look at this
http://en.wikipedia.org/wiki/Leibniz_integral_rule#Proof_of_basic_form

Answer 3

That's it. Thanks