How to I approach the following problem?
Suppose $\phi (x) : [0,5] \rightarrow [0,1] $ is an IVP given by:
$$\phi (x) := \left \{ \begin{array}{l} x, \forall x \in [0,1] \\ 1, \forall x \in (1,5] \end{array}\right. $$
Find the solution $f(x) : [1,5) \rightarrow \Re $ of the initial value problem
$$\frac{df}{dx} = \phi (x) $$ where $$ f(0)=1 $$
and show your solution is differentiable on $(0,5)$.