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Here is an example you can look at.

http://www.sagenb.org/home/pub/1927/

Here is an example you can look at.

http://www.sagenb.org/home/pub/1927/

Edit: If you need to preload the function use the following link

http://ask.sagemath.org/question/1072/preload-defined-functions-for-later-use

Here is an example you can look at.

http://www.sagenb.org/home/pub/1927/

Edit: If you need to preload the function use the following link

http://ask.sagemath.org/question/1072/preload-defined-functions-for-later-use

Edit2:

Sorry for the delay. Here is the full solution to your question

def changevar(f, eqn, newvar):
    dx = diff(eqn.rhs(),newvar)
    return f.substitute(eqn)*dx 
var('u')
assume(x>0)
xmin=0
xmax=2
eqn=sqrt(u-1)
limits(x)=solve(eqn==x,u)[0].rhs()
limits(2)
ans=changevar(x*cos(x^2+1), x==eqn, u)
integrate(ans,(u,limits(xmin),limits(xmax))).n()