Mathematics

Problem

Let

f(t)=t^{2}+1

, and define two functions

G(x)=1+\displaystyle\int_{0}^{x} f(t)\,dt

and

H(x)=5+\displaystyle\int_{0}^{x} f(t)\,dt

. Which of the following best describes the graph of

H

relative to the graph of

G

? a)

H

is obtained by translating the graph of

G

upward by

4x

units. b)

H

is obtained by translating the graph of

G

to the right by

4

units. c)

H

is obtained by translating the graph of

G

upward by

4

units. d)

H

is obtained by translating the graph of

G

downward by

4

units.