The answer is Agent 99, no matter which four integrals are chosen.
Here are the answers to the sixteen definite integral problems:
How does it work?
The restriction in picking the four integrals to evaluate forces the student to choose exactly one number from each row and column.
So, the sum of the four numbers is really the sum of the 8 numbers of the addition table (the blue numbers in the row and column headings below).
The sum of 40 + 0 + 4 + (1/3) + (2/3) + (-2) + 12 + 44 = 99.
| + | 40 | 0 | 4 | 1/3 |
|---|---|---|---|---|
| 2/3 | 40 2/3 | 2/3 | 4 2/3 | 1 |
| -2 | 38 | -2 | 2 | -1 2/3 |
| 12 | 52 | 12 | 16 | 12 1/3 |
| 44 | 84 | 44 | 48 | 44 1/3 |