calculus and analysis - Incorrect result for integral of series

Here's an integral that comes up in calculating the number of domino tilings of the plane:

Integrate[Log[(Sin[k] + Sqrt[1 + Sin[k]^2])^2], {k, 0, π}]
(* 4 Catalan *)

And here is the same result with a trivial addition:

Integrate[Log[(Sin[k] + Sqrt[1 + Sin[k]^2])^2] + x, {k, 0, π}]
(* 4 Catalan + π x *)

But if I change the integrand into a series, the result is different:

Integrate[Log[(Sin[k] + Sqrt[1 + Sin[k]^2])^2] + x + O[x]^2, {k, 0, π}]
(* 4 Catalan + π (x + Log[2]) *)

Note the additional term independent of x. Surely this is a bug?

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I'm using Mathematica 11.0.1 on Windows 10 (64-bit).