How to treat a constant when integrating I am wondering what to do when coming across an integral like this where $a$ is a constant:
$$\int^{1000}_a (x-a){1\over1000}dx $$
As far as I can see, it should be ok to do this: 
$$ \left.{1\over 1000} \left({{{x^2}\over2} -ax}\right)\right|^{1000}_a$$
But the book I am using does:
$$ \left.{1\over 1000} \left({{(x-a)^2}\over2}\right)\right|^{1000}_a$$
Which also seems correct, but is different. How does one decide which way to integrate? (The actual question in the book is regarding expected value of probability, and I can copy it in full if it makes a difference.)

The two expressions are different only by a constant. When you take bounds, the constant vanishes, giving the same result.
