List of top Real Analysis Questions on Lebesgue Measure and Integration

Let \( C \) denote the Cantor set and \( f: [0,1] \to \mathbb{R} \) be defined as follows:
\[ f(x) = \begin{cases} x^{2026} & \text{for } x \in C \\ \cos(\pi x) & \text{for } x \in \left[0, \dfrac{1}{2}\right] \setminus C \\ \sin(\pi x) & \text{for } x \in \left[\dfrac{1}{2}, 1\right] \setminus C \end{cases} \]
The value of the Lebesgue integral of \( f(x) \) over the interval \( [0,1] \) is equal to