Let g be continuous on [2,8] and suppose g(t)>0 for 2<t<5 and g(t)<0 for 5<t<8. Define G(x)=∫2xg(t)dt. Which statement best describes the behavior of G on the interval (2,8)?
a) G is increasing everywhere on (2,8) because the interval of integration is expanding.
b) G is constant on (2,5) and decreases on (5,8).
c) G is increasing on (2,5) and decreasing on (5,8).
d) G is decreasing on (2,5) and increasing on (5,8).