How to Apply Leibnitz Rule When Integration Limits Depend on a Variable?

[Economist2008]

Does anybody know, how to find the derivative of the F with respect to a? As far as I know the Leibnitz rule is only applicable, when the integration limits do not depend a. But what happens, when one of the limits is a function of a?

F(a,x)=\int ^{c+h(a)}_{c} f[g(a,x)] dx

Thank you so much!

 

[quadraphonics]

What I know as "Leibnitz's Rule" covers cases where both limits depend on the variable of differentiation:

http://mathworld.wolfram.com/LeibnizIntegralRule.html

 

[Economist2008]

Ups, the books I looked at didn't cover this case.
Thank you very much!