Question 189
Determine the continuous and increasing functions $f:[0, \infty) \rightarrow \mathbb{R}$ for which
$$
\int_{0}^{x+y} f(t) \mathrm{d} t \leq \int_{0}^{x} f(t) \mathrm{d} t+\int_{0}^{y} f(t) \mathrm{d} t
$$
for all $x, y \in[0, \infty)$.
$$
\int_{0}^{x+y} f(t) \mathrm{d} t \leq \int_{0}^{x} f(t) \mathrm{d} t+\int_{0}^{y} f(t) \mathrm{d} t
$$
for all $x, y \in[0, \infty)$.