Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that $$f(x) = 1 - f(2 - x)$$ Which one of the following options is the CORRECT value of $\int_0^2 f(x)dx$ ?

Let the integral be:

Using the definite integral property $\int_a^b f(x)\,dx = \int_a^b f(a+b-x)\,dx$, where $a = 0$ and $b = 2$:

Adding equations (1) and (2):

From the given relation $f(x) = 1 - f(2 - x)$, we have:

Substituting this into the sum of integrals:

Thus, the correct option is (B).