you know that x² - 1 = (x + 1) (x - 1); so let's replace it

= integral [(x - 1) (x + 1) / (x + 1)] dx; the (x + 1) on the numerator and denominator will disappear, so

= integral [x - 1] dx; then

= x²/2 - x; since we have to evaluate from x = 1 to x = 2; then

= (2)² / 2 - 2 - (1² / 2 - 1)

= 2 - 2 - (1 / 1)

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= -1
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