Probability from a piecewise-linear density with unknown middle height

Let $X$ be a continuous random variable with the probability density function

$$f(x)=\begin{cases}\frac x8, & 0<x<2,\ \frac k8, & 2\le x\le4,\ \frac{6-x}8, & 4<x<6,\ 0, & \text{otherwise,}\end{cases}$$

where $k$ is a real constant. Then $P(1<X<5)$ equals __________________