Which expression equals where is continuous and are differentiable functions of ?

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Which expression equals

\displaystyle \frac{d}{dx}\left(\int_{g(x)}^{h(x)} f(t)\,dt\right)

where

f

is continuous and

g,h

are differentiable functions of

x

? (a)

f\big(h(x)\big)-f\big(g(x)\big)

(b)

(h'(x)-g'(x))\,f(x)

(c)

f\big(h(x)\big)\,h'(x)-f\big(g(x)\big)\,g'(x)

(d)

f\big(h(x)\big)\,h'(x)+f\big(g(x)\big)\,g'(x)