Which of the following properties of integrals is always true?
∫[f(x)g(x)]dx=∫f(x)dx⋅∫g(x)dx\int [f(x)g(x)] dx = \int f(x) dx \cdot \int g(x) dx∫[f(x)g(x)]dx=∫f(x)dx⋅∫g(x)dx
∫abf(x)dx=∫baf(x)dx\int_a^b f(x) dx = \int_b^a f(x) dx∫abf(x)dx=∫baf(x)dx
∫acf(x)dx=∫abf(x)dx+∫bcf(x)dx\int_a^c f(x) dx = \int_a^b f(x) dx + \int_b^c f(x) dx∫acf(x)dx=∫abf(x)dx+∫bcf(x)dx
If ∫abf(x)dx=0\int_a^b f(x) dx = 0∫abf(x)dx=0, then f(x)=0f(x) = 0f(x)=0 for all xxx in [a,b][a, b][a,b].