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(d/dt)∫f(x,t)dx

then they simplify it to:

∫[∂f(x,t)/∂t]dx

I mean, it sort of makes sense to me, because the integral will be a function of t only so the (d/dt) is fine, but when you bring it inside the integral f(x,t) is a function of both t and x, so a partial is needed... but why is it ok to do this?