I've been solving problems from the book by DeGroot and Schervish and I can't understand why m is the upper limit of integration in the solution to this problem. Why not the lower one?
Here is the problem:
Suppose that a random variable X has a continuous distribution for which the p.d.f. f is as follows:
$f(x) = 2x$ for $ 0< x <1, 0 $ otherwise
Determine the value of $d$ that minimizes $E(|X − d|)$.
Here is the solution:
$$ \int_0^m 2x \, dx=0.5 $$
Thank you very much in advance.