You have indicated the integral and the integrand correctly. The integral is not a function of x because it is a definite integral, which means that the x is a dummy variable that does not feature in the result of the integral. To take a simple example,

. The integral there is not a function of x because it is just a constant, 1/2. When you integrate a function of two variables, such as

, the integral is a function of t, but because it is a definite integral, it is not a function of x.

There is a theorem which says that you can push the operation of differentiation with respect to t past the integral sign. But when you do so, it changes from an ordinary differentiation to a partial differentiation.