The Leibniz ruleThe integral is a function of the parameter t. Show that the derivative of F is given by This relation is also known as the Leibniz rule. 
Proof:
We have,
Now,
Since f(x,t) is essentially constant over the infinitesimal intervals a < x < a + Δa and b < x < b + Δb, we may write
Taking the limit as , we get
or,
