Evaluating $ \int_0^1 \int_y^1 \sqrt{1+x^2} dx dy $ $$   \int_0^1 \int_y^1 \sqrt{1+x^2} dx dy $$
I've tried switching the order as per fubini theorem to $\int_y^1 \int_0^1 \sqrt{(1+x^2)} dy dx$
and managed to get $\int_y^1 \sqrt{(1+x^2)} dx$ but am stuck there. How do i continue integrating?

$\displaystyle I=\int \sqrt{1+x^2}dx$
$\displaystyle =\int \sqrt{1+\sinh^2u}\cosh udu$ [Substitute $x=\sinh u, dx=\cosh udu$]
$\displaystyle=\int \cosh^2udu$
$\displaystyle=\frac 1 2 \int (\cosh 2u+1)du$
$\displaystyle=\frac 1 2(\frac 1 2\sinh u+u)+C$
