Calculate the definite integral by referring to the figure with the indicated areas.
\[
\int_{c}^{a} f(x) d x
\]

Area $A=7.667$
Area $C=51: 638$

Area $B=5.867$
Area $\mathrm{D}=14.833$
\[
\int_{c}^{a} f(x) d x=\square
\]
(Type an integer or a decimal rounded to three decimal places as needed.)

Step 1 ：The definite integral of a function from a to b is the signed area between the function and the x-axis, from a to b. The sign of the area depends on whether the function is above or below the x-axis. If the function is above the x-axis, the area is positive. If the function is below the x-axis, the area is negative.

Step 2 ：In this case, we are given the areas of four regions, A, B, C, and D. We are asked to find the integral from c to a. Looking at the figure (which is not provided here), we need to determine which of these areas are between the function and the x-axis from c to a, and whether each area should be considered positive or negative.

Step 3 ：Without the figure, we can't determine this. However, if we assume that the areas A and C are above the x-axis and the areas B and D are below the x-axis, and that all four areas are between c and a, then the integral from c to a would be A + C - B - D.

Step 4 ：Given that A = 7.667, B = 5.867, C = 51.638, D = 14.833, we can calculate the integral from c to a as \(A + C - B - D = 7.667 + 51.638 - 5.867 - 14.833\)

Step 5 ：Calculating the above expression gives us the result 38.605

Step 6 ：Final Answer: The definite integral of the function from c to a is \(\boxed{38.605}\)