Let F(x)=∫3xf(t)dt, where f is continuous. Which of the following statements must be true for all x in the domain of f?
a) If f(x)<0, then F is increasing at x.
b) F is increasing for all x because f is continuous.
c) If f(x)>0, then F is increasing at x.
d) If f(x)=0, then F is increasing at x.