(x^3+2x^2-15x+1)/(x^2+2x-15) from 0 to 7

I assume you want an integral?

First, do a simple long division to get

x + 1/(x^2+2x-15)
= x + 1/8(x-5) + 1/8(x+3)

Now it's simple, if you recall that

∫1/u du = ln u