Suppose f:[a,b]→Rf:[a,b]\to\mathbb{R}f:[a,b]→R is continuous and ∫axf(t) dt = ∫xbf(t) dtfor all x∈[a,b].\int_a^x f(t)\,dt \;=\; \int_x^b f(t)\,dt \quad \text{for all } x \in [a,b].∫axf(t)dt=∫xbf(t)dtfor all x∈[a,b]. Then f(x)f(x)f(x) must be
A non-zero constant
A linear function
Identically zero
An odd function about a+b2\dfrac{a+b}{2}2a+b
