The following command in Version 9.0.1:

N[Integrate[x^50*Sin[x], {x, 0, 1}]]

gives $1.4615\times 10^{48}$ which is way off from the correct solution which is between $0$ and $0.5$.

Interestingly the indefinite integral comes out correct and if you increase the precision Mathematica gives an error and the following number: $0.0163$. The same result is given by NIntegrate.

What exactly is the problem here, is this a known issue and is there a workaround?