okay, i don't know yet what those theorems are.. Ü

but can you check this out.. (i think, this disproves the statement)

$\displaystyle \int_0^1 x^n \cdot (n+1) dx = 1$

and also

$\displaystyle \int_0^1 x^n \cdot (nx+2x) dx = 1$

and there, $\displaystyle f(x) = n+1 \neq (nx+2x) = x(n+2) = g(x)$

or, i just misunderstood the statement.. Ü