Let \(f: [0, 1] \rightarrow \mathbb{R}\) be a continuous functionProve the following statement:

For every \( \epsilon > 0 \), there exists a \(\delta > 0\) such that if \(x, y \in [0, 1]\) and \(|x - y| < \delta\), then \(|f(x) - f(y)| < \epsilon\).