Fourier transform formulation of the dirac delta

[ehrenfest]

I have seen two formulations of the dirac delta function with the Fourier transform. The one on wikipedia is
\int_{-\infty}^\infty 1 \cdot e^{-i 2\pi f t}\,dt = \delta(f)

and the one in my textbook (Robinett) is

1/2\pi \int_{-\infty}^\infty 1 \cdot e^{-i f t}\,dt = \delta(f)

I do not understand how they are equivalent? How can you just take the 2pi out of the integral?

[George Jones]

It's a simple change of variable: if t'=2\pi t, then dt=dt'/2\pi.