Step-by-Step Solution
Key Concept: The greatest integer function (floor function) applied to a function bounded between 0 and 1 yields 0.
Since $x\sin(\pi x) \in (0,1)$ for all $x \in (0,1)$, we have $[x\sin(\pi x)] = 0$ for $x \in (0,1)$. Therefore, $I = 2\int_0^1 0dx = 0$.
Correct Answer: 0