It seems that NIntegrate does not handle vector-valued InterpolatingFunction. Strangely enough, Integrate works fine:
NIntegrate
InterpolatingFunction
Integrate
dataX = Table[{n, {n, 2 n}}, {n, 0, 10}]; dataF = Interpolation[dataX]; Integrate[dataF[x], {x, 0, 10}]
