Given an intergral $$ \int_{a(t)}^{b(t)} f(t, x) dx $$ What is the fomula to of its derivation? $$ \frac{\partial}{\partial t} \int_{a(t)}^{b(t)} f(t, x) dx $$
Would someone please give me a link to the fomula and its derivations?
EDIT:
The answer is $$ \int_{a(t)}^{b(t)} f'_t(t, x)dx + f(t, b(t)) b'_t(t) - f(t, a(t)) a'_t(t) $$ and here(Leibniz_integral_rule) is the reference.
Many thanks to André Nicolas's comment!