Bugs in Integral of Bessel Function?

Questions
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1

Integrate[(Sum[BesselJ[n, r], {n, 0, 10}])^2*r, {r, 0, [Infinity]}]

Result is -9.20481
The integral of square of Sum of BesselJ function from 0 to 10 order but give a negative result. This shouldn’t be, because it is a real function and after square it is all greater or equal zero and r is also positive or zero. The result should be positive. Anything could be wrong with Mathematica?

2

Integrate[(Sum[BesselJ[n, r], {n, 0, 10}])^2*r, {r, 0, \[Infinity]}, GenerateConditions -> True]

reports that the integral does not converge. I guess with the default setting for GenerateConditions, it is not so careful.

3
Open in Wolfram Cloud ↗

Draw your own conclusions.