Answer is: option4

Solution:

Bottom Shaded Region:

• Bounded by \( f(x) \) (above the x-axis) and the x-axis \( (y = 0) \).
• The area is:
  \( \text{Area}_{\text{bottom}} = \int_0^a f(x)\,dx \)

Top Shaded Region:

• Bounded by \( y = b \) (above \( g(x) \)) and \( g(x) \).
• The area is:
  \( \text{Area}_{\text{top}} = \int_0^a (b - g(x))\,dx \)

Total Shaded Area:

• The total area is the sum of the bottom and top areas:

\[ \text{Total Area} = \text{Area}_{\text{bottom}} + \text{Area}_{\text{top}} = \int_0^a f(x)\,dx + \int_0^a (b - g(x))\,dx \]

\[ \text{Total Area} = \int_0^a \left(f(x) + b - g(x)\right)\,dx \]

\[ \text{Total Area} = \int_0^a \left(b - g(x) + f(x)\right)\,dx \]

This corresponds to option (D).