Evaluate the integral using methods of improper integrals

Question

∫(0 to 4)dx/(x²-x-2)

For this question, I would split the integral so that it would be ∫(0 to 1) dx/(x²-x-2)+ ∫(1 to 4) dx/(x²-x-2) right?

So ∫(0 to 1)dx/(x²-x-2) = lim (t→1^-) ∫(0 to t) dx/(x²-x-2),

And ∫(1 to 4) dx/(x²-x-2) = lim (t→1⁺) ∫(t to 4) dx/(x²-x-2).

And then I would use Partial Fraction Decomposition and factor the denominator so that (x²-x-2)=(x-2)(x+1)

So A/(x-2) + B/(x+1) and 1=A(x+1)+B(x-2)?

Answer 1

Find the improper interval from 0 to 4 and identify the cauchy value principle for does not converge.