Here's the question you clicked on:
henpen
\[\frac{d}{dx} \int_a^bf(x)dt=\int_a^b\frac{df(x)}{dx}dt\] Why is the equality correct?
http://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign It's to do with this, but the article didn't help me much
did you look at this http://en.wikipedia.org/wiki/Leibniz_integral_rule#Proof_of_basic_form