Let c be a positive real number. In the rectangular coordinate plane, the line $y = c$ and the graph of the function $y = f ( x )$ are given below.
The area of the blue region is 2 square units more than the area of the yellow region.
$$\int _ { 1 } ^ { 4 } f ( 2 x ) d x = 28$$
Given that, what is the value of c?\\
A) 8\\
B) 9\\
C) 10\\
D) 11\\
E) 12