Is the following true?
If $$\int_{0}^{x}f(t)\,dt \leq \int_{0}^{x} c \,dt =cx $$ for all $x>0$, $x$ is real number, and $c$ is some fixed constant,
then
$$f(t) \leq c$$ for all $t>0$?
EDIT: I should said that $f(t)$ is positive function on $t>0$, and $f(t_{1}+t_{2})\geq f(t_{1})+f(t_{2})$, for all $t_{1},t_{2}>0$ if this helps!