## Differentiation of integrals and integration(?)

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
 PhysOrg.com science news on PhysOrg.com >> 'Whodunnit' of Irish potato famine solved>> The mammoth's lament: Study shows how cosmic impact sparked devastating climate change>> Curiosity Mars rover drills second rock target
 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus
 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.