Explanation:

Alright, let’s get straight to it.

- The integral is ?¹_-1(x - 2 + x) dx.

- Let’s tidy up inside: x - 2 + x = 2x - 2.

- So the integral becomes ?¹_-1(2x - 2) dx.

- Split it: ?¹_-12x dx - ?¹_-12 dx.

- ?2x dx from -1 to 1 = 2 * [x²/2] from -1 to 1 = [x²] from -1 to 1. That’s 1 – 1 = 0.

- ?2 dx from -1 to 1 = 2*[x] from -1 to 1 = 2*(1 – (-1)) = 4.

- So the whole thing is 0 – 4 = –4.

Now the options:

Option:1, 7

Option:2, 5

Option:3, 4

Option:4, 6

The answer is not among the options listed. The correct value is –4.

Just so it’s clear: None of the options match the calculated answer (–4). If you need the correct option, it’s not present among the four you gave.