[Note:] The error described here has been corrected in the meantime in response to this question.
When checking wikipedia on substition they say that \int f(g(t))g'(t) dt = \int f(x)dx with x = g(t). Which is true. However, when checking example 1 on the page ( http://en.wikipedia.org/wiki/Integration_by_substitution)
They say that when evaluating $\int x\cos(x^2 +1) dx$ in example one, they use the substition $u=x^2 + 1$ and say that they use the rule mentioned above from right to left, however this isn't the case right? Aren't they using that rule from left to right?