Let $ X = C[0,1] $ with the supremum norm $ || \cdot ||_\infty $. Consider the functional $ \phi $ defined for $ f \in X $ by $$ \phi(f) = \int_0^\frac{1}{2} f(x) dx - \int_\frac{1}{2}^1 f(x) dx .$$ Show that if $ f \in X $ with $ ||f|| = 1 $ then $ |\phi(f)| < 1 $.
A previous part of this question was to show that $ \phi $ is a bounded linear functional with norm 1 which I have done already. But I do not know how to show that $ |\phi(f)| < 1 $. Any help or hints would be appreciated.