As I said
Please make sure I have fixed them correctly.
Did you verify that the expressions are correctly parenthesized and Sqrt5 should be Sqrt[5]?
I did find something interesting. If I first evaluate
Integrate[lhs, {x, -2, 2}]
and then evaluate
Integrate[lhs, {x, 0, xSol}]
The result is a simpler expression that is numerically equivalent
(* 1/240 (-3 Sqrt[5 (35 - 13 Sqrt[5] + Sqrt[30 (65 - 29 Sqrt[5])])] + 8 π) *)
This odd behavior is reproducible (at least for me on "12.3.1 for Mac OS X x86 (64-bit) (June 19, 2021)"). I will report it to Wolfram support.
