Differentiation of integrals and integration(?)

[ShayanJ]

I heard that the formula below can be used to evaluate some kinds of integrals but I can't find what kinds and how to do it.Could someone name those kinds and also the procedure?

$\frac{d}{dx} \int_{a(x)}^{b(x)} f(x,t) dt = f(x,b(x)) b'(x) - f(x,a(x)) a'(x) + \int_{a(x)}^{b(x)} \frac{\partial}{\partial x} f(x,t) dt$


Thanks

 

[micromass]

http://en.wikipedia.org/wiki/Leibniz_integral_rule

 

[ShayanJ]

That doesn't contain what I wanted.
I have seen another page from wikipedia too.That one contains some integration using the formula but I can't understand the general procedure.