Answer
$\dfrac{d}{d x} \int_a^{u(x)}f(t) dt =f((u(x)) \cdot u'(x)$
Work Step by Step
Consider the definition of The fundamental Theorem of Calculus such as:
$\dfrac{d}{d x}\int_a^{u(x)}f(t) dt= [\dfrac{d}{d(u(x))}\int_a^{u(x)}f(t) dt](\dfrac{d(u(x))}{d x})$ (Apply chain rule)
Thus, we have $\dfrac{d}{d x} \int_a^{u(x)}f(t) dt =f((u(x)) \cdot u'(x)$
