You need to remember the Leibniz rule for a differentiable function `f(v,x)`  such that:

`d/(dx) int_(a(x))^(b(x)) f(v,x) dv = int_(a(x))^(b(x)) (del f(v,x))/(del x) dv`

In this case, the limits `a(x)`  and `b(x)`  are constants, but if `a(x)`  and `b(x)`  are not constants, hence, the extended Leibniz rule is the following, such that:

`d/(dx) int_(a(x))^(b(x)) f(v,x) dv = int_(a(x))^(b(x)) (del f(v,x))/(del x) dv + b'(x)(f(b(x),x)) - a'(x)(f(a(x),x))`

Hence, you may use either the extended form, or the simpler form of Leibniz rule, depending on the nature of limits `a(x)`  and `b(x).`