Possible Duplicate:
Let $f:[0,1]\to\mathbb R$ be continuous such that $f(t)\geq 0$ for all $t$ in $[0,1]$. What can be said about $g(x):=\int_0^x f(t)\,dt$?
Let $f:[0,1] \to\mathbb{R}$ be continuous such that $f(t) ≥0$ for all t in $[0, 1]$. Define $g(x) = \int_0^xf(t) \, dt$ then which is true?
1 $g$ is monotone and bounded
2 $g$ is monotone, but not bounded
3 $g$ is bounded, but not monotone
4 $g$ is neither monotone nor bounded
I think either 1 or 2 is true as I get it is monotone but not sure about boundedness