Explanation:

Let’s go step by step:

- You’re given:

   - f'(x) = x² + 2

   - g(x) = 2x - 3

- But to find (fg)(1), you need values of f(1) and g(1), not f'(x).

- First, let’s find f(x) by integrating f'(x):

   - ?(x² + 2) dx = (1/3)x³ + 2x + C, where C is a constant.

   - f(x) = (1/3)x³ + 2x + C

- Calculate f(1):

   - f(1) = (1/3)(1)³ + 2(1) + C = 1/3 + 2 + C = 7/3 + C

- Calculate g(1):

   - g(1) = 2(1) - 3 = -1

- So (fg)(1) = f(1)·g(1) = (7/3 + C)(-1) = -7/3 - C

Now check all options:

- 1) 3

- 2) 1

- 3) -2

- 4) -3

Since C is unknown, (fg)(1) cannot be found precisely unless more info is given about f(x) or C!

- None of the options can be confirmed as correct without knowing C.

If you had some extra information, like f(0)=0, you could find C, but with current info there’s not enough to solve for a specific value.

None of the options are correct given only the data above.