grals to find $\int_{1}^{8} f(x) d x$ for the following function. Use the properties of definite in $f(x)=\left\{\begin{array}{ll}6 x+5 & \text { if } x \leq 4 \\ -0.2 x+3 & \text { if } x>4\end{array}\right.$ \[ \int_{1}^{8} f(x) d x=\square \] (Simplify your answer.)

Step 1 ：The integral of a piecewise function from a to b can be found by breaking the integral into two parts at the point where the function changes, which is at x=4 in this case.

Step 2 ：So, we need to find the integral of the function from 1 to 4 and from 4 to 8, and then add these two results together.

Step 3 ：For the function \(f(x) = 6x + 5\) from 1 to 4, the integral is 60.

Step 4 ：For the function \(f(x) = -0.2x + 3\) from 4 to 8, the integral is 7.2.

Step 5 ：Adding these two results together, we get a total integral of 67.2.

Step 6 ：Final Answer: The integral of the function from 1 to 8 is \(\boxed{67.2}\).