Find the area under the graph of $f$ over the interval $[1,3]$. \[ f(x)=\left\{\begin{array}{ll} 2 x+1, & \text { for } x \leq 2 \\ 7-\frac{1}{2} x, & \text { for } x>2 \end{array}\right. \] The area is (Type an integer or a simplified fraction.)

Step 1 ：The function is defined piecewise, so we need to split the interval into two parts: [1,2] and (2,3].

Step 2 ：We then integrate the function over these two intervals separately.

Step 3 ：For the interval [1,2], the function is defined as \(f(x) = 2x + 1\). The area under this part of the function is 4.

Step 4 ：For the interval (2,3], the function is defined as \(f(x) = 7 - 0.5x\). The area under this part of the function is 5.75.

Step 5 ：The total area under the graph of the function over the interval [1,3] is the sum of the areas under the two parts of the function over their respective intervals.

Step 6 ：Adding these two areas together gives a total area of 9.75.

Step 7 ：Final Answer: The area under the graph of the function over the interval [1,3] is \(\boxed{9.75}\).