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integral question


Hello,
I have a question and was wondering if someone could help me with it.  This
is a general vector calculus problem, not specific to Mathematica.  I have a
simple integral as follows:
Given r^2= x^2+y^2, solve Integral[r^2, dr] from point1 (0,0) to point2
(1,1), which would be evaluated from r=0 to r=sqrt[2] and gives answer =
2*sqrt[2]/3.
The above is pretty simple, however, I am not sure how to formulate the
problem when I convert the 'dr' back to cartesian coordinates as follows:
Integrate [x^2+y^2, d????] and the limits???  WHat should 'dr' be in terms
of dx? if my integrand is directly x^2+y^2.  It cannot be a double integral,
since the original problem was a single integral, but then how do you solve
this??
Can anyone help?

thanks!






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