Mathematics

Problem

Let

f

be a continuous function with

f(t)>0

for

0<t<5

and

f(t)<0

for

t>5

. Define

g(x)=\displaystyle\int_{0}^{x} f(t)\,dt

. Determine the interval(s) on

(0,7)

where

g

is increasing, and justify your answer in one sentence.