[johnm693]

x(t):=2*cos(t);
y(t):=2*sin(t);
integrate((x(t)+y(t)^2)*sqrt(diff(x(t),t)^2+diff(y(t),t)^2),t);

Maxima encountered a Lisp error:

The value 2 is not of type LIST.

Automatically continuing.
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(%i6) bug_report ();

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(%o6) ""

Yes, I agree that there is a bug but just in case you have not noticed it, the bug does not show up if you use trigsimp:

(%i3) integrate(trigsimp((x(t)+y(t)^2)*sqrt(diff(x(t),t)^2+diff(y(t),t)^2)),t);
                           sin(2 t)
(%o3)               4 (t - --------) + 4 sin(t)
                              2

The first "bad" commit 475ce5d831112

https://sourceforge.net/p/maxima/code/ci/475ce5d8311126f389830b2c8f94823724bcacc5

Rename special variables a, b, c, d to *a*, *b*, *c*, *d* to prevent
collisions in other files. (I'm pretty sure these are meant to be
local to this file.)
Test suites passes.

Modified   src/sin.lisp

Thanks for this report. Fixed by commit [84c328a5]. Closing this report.