A function $y(x)$ is defined in the interval $[0, 1]$ on the $x – $ axis as
$$y(x) = \left\{\begin{matrix} 2& \text{if} & 0 \leq x < \frac{1}{3} \\ 3& \text{if}& \frac{1}{3} \leq x < \frac{3}{4} & \\ 1 & \text{if} & \frac{3}{4} \leq x \leq 1& \end{matrix}\right.$$
Which one of the following is the area under the curve for the interval $[0, 1]$ on the $x – $ axis?
- $\frac{5}{6}$
- $\frac{6}{5}$
- $\frac{13}{6}$
- $\frac{6}{13}$