21\int_{0}^{1}f(x)\text{d}x = \int_{0}^{1/2}f(x)\text{d}x + \int_{1/2}^{1}f(x)\text{d}x
= \int_{0}^{1/2}f(x)\text{d}x + \int_{0}^{1/2}f(x+ \frac 1 2)\text{d}x
= \int_{0}^{1/2}f(x)\text{d}x + \int_{0}^{1/2}\left ( 1-f(x)\right )\text{d}x = \int_{0}^{1/2}\text{d}x = \boxed{\frac 1 2}
But in an exam like engineering entrances we can just set f(x)= \frac 1 2 \forall x \in \mathbb{R} and get the required answer without any mathematical effort :)
