Question 183
Determine the continuous increasing functions $f: [0, \infty) \to \mathbb{R}$ satisfying
$$
\int_{0}^{x+y} f(t) dt = \int_{0}^{x} f(t) dt + \int_{0}^{y} f(t) dt,
$$
for all non-negative real numbers $x$ and $y$.
$$
\int_{0}^{x+y} f(t) dt = \int_{0}^{x} f(t) dt + \int_{0}^{y} f(t) dt,
$$
for all non-negative real numbers $x$ and $y$.