Is taking the derivative inside this integral acceptable?

I have run into an integral where I take the partial derivative of x when the upper limit of the integral is x. This is how I solve it but I am not sure if this is correct. Can someone please check? Thank you!
$$ frac{partial}{partial x}int_0^xf(t)dt=int_0^xfrac{partial f(t)}{partial x}dt=0 $$