prove g(x)=x^2 + 2x - 5 is uniformly continuous on [0,3].

proof: Let e>0 and choose delta=e/3. If |y-x|< delta and x,y e[0,3] then |g(y)-g(x)| = |(y^2 +2y -5)-(x^2 +2x -5)|=|y^2 -x^2 +2y-2x|=

|y(y+2) - x(x+2)| < 3|y-x| < (3)delta = e.

Did i do the proof right? I get confused when an interval is given such as [0,3]. What is the difference if the interval was [0,3)? How does that effect the proof?