I am studying for exams and am stuck on this problem.
Let $f:[0,1]\rightarrow \mathbb R$ be continuous such that $f(t)\geqslant 0$ for all $t$ in $[0,1]$. Define $g(x)=\int_{0}^{x}f(t)dt$.Then which of the following is correct?
(a) $g$ is monotone and bounded,
(b) $g$ is monotone but not bounded,
(c) $g$ is bounded but not monotone,
(d) $g$ is neither monotone nor bounded.
I take $f(t)=t+1$ and proceed according to the given condition. I see that g is bounded and monotone. Am I right? I want a better way to approach the problem. Please help.