Displacement of particle motion

A particle moves along a line so tat its position at any time t>= 0 is given by the function

$\displaystyle s(t)= t^2-3t+2$

where s is measure in meters and t is measured in seconds

Find the displacement in meters and t is measured in seconds

The book gives this:

The displacement of the object over the time inverval from t to tx (they used delta t but this is easier for the purpose) is

delta S = f(t + tx) - f(t)

I did what I needed, by acting as this is a difference quotient without a limit or denominator, to solve normally and got this:

$\displaystyle tx^2 + 2txt - 3xt$

The answer, however, is 10.

I'm sure there is some reason why the above (as in my answer) = 2t. But, I don't know how.

Thank you!.