Let be continuous on and define by

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

Problem

Let

f

be continuous on

\mathbb R

and define

g

g(x)=\displaystyle\int_{1}^{x} f(t)\,dt

. Which of the following statements must be true for every real number

x

? (a)

g'(x)=\displaystyle\int_{1}^{x} f'(t)\,dt

(b)

g'(x)=f(x)

(c)

g(x)=f'(x)

(d)

g'(x)=f'(x)