f,g: [a,b]---> R

f(x)>g(x) for every x at [a,b]

which of these statements are true? and why?

1. if f and g are continous at (a,b), and f is bounded at [a,b] - so sup f((a,b))>sup g((a,b)).

2. if f and g are continous at [a,b], so sup f([a,b])>sup g([a,b]).

thanks