#### Answer

$\dfrac{d}{d x} \int_a^{u(x)}f(t) dt =f((u(x)) \cdot u'(x)$

#### Work Step by Step

Here, we have $\dfrac{d}{d x}\int_a^{u(x)}f(t) dt= [\dfrac{d}{d(u(x))}\int_a^{u(x)}f(t) dt](\dfrac{d(u(x))}{d x})$
This implies that
$\dfrac{d}{d x} \int_a^{u(x)}f(t) dt =f((u(x)) \cdot u'(x)$
The answer can be checked in a CAS (e.g. Maple).