I agree with the Paper's answer. It seems to me that it would be very difficult to get the integral wrong if you managed to partial frations correctly. What did you get for the partial fraction decomposition?
2 - x + what/(x+5) - what/(x-5)
Get everything on the left side and look at it. Gather like terms until it looks like a quadratic. What happens when the discriminant is less than zero?
You have x = 2.
From the line, you can determine the coordinates of the point of tangency. Substitute x = 2 and y = ????? into the cubic.
From the slope of the line, you can determine the value of the first derivative of the cubic. Substitute x = 2 into the derivative and y`(2) = the slope of the line.
You may have a little algebra after that.
Those are the workings.