Integrate[y, {t, .5, 1}]

I get the following answer:

(0.34657*x1/sigma^2)

OK, so far, so good. It appears that I can generate an answer with a
non-numeric parameter. Note that I am looking for an answer in terms
of x1.

But when I try

 q=Exp[-(x1-t)^2/2*sigma^2*t]

Integrate[q, {t, .5,1}]

Now Mathematica does not solve this integral, it just repeats the
command

I am trying to get an expression in terms of x1. Why do I get a
statement like this instead of an answer?  There is something about
the functional form of the integrand that is causing the problem, I
just don't know what it is.