For a continuous function

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

Problem

h

, a constant

c

satisfies

\int_{2}^{5}\bigl(h(x)+c\bigr)\,dx = \int_{2}^{5}h(x)\,dx

for every continuous function

h

. Which of the following statements about

c

is true? (a)

c

can be any real number (b)

c

must equal

h(3)

(c)

c=0

(d)

c=-\dfrac{1}{3}\displaystyle\int_{2}^{5} h(x)\,dx