What is the form of “Leibniz Rule” for integral of f(x,a,b) from a to b? x is variable and derivation is done in respect of a and b. Since the “Leibniz Rule” for derivation of finite integrals is presented in literature for f(x,α) with limits as a(α) and b(α) and derivation in respect of α, I have wondered. Please help me.

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,...