Inverse Fourier transform of a step-function

The function $h(t)$ will be the inverse Fourier trasform of $H(k)$, i.e. 
\[h(t)=\int_{\infty}^{\infty} H(k)e^{2\pi i t k}dk=\int_0^6 e^{2 \pi i tk} dk\]
\[=\frac{e^{2 \pi itk}}{2\pi i t}\big |_{0}^{6}=\frac{1}{2\pi i t} (e^{12\pi i t}-e^{0})\]
\[-\frac{i}{2\pi t} (e^{12\pi i t}-1)=-\frac{i}{2\pi t} (\cos  (12 \pi t)+i \sin (12 \pi t)-1)\]


I am using the definiton of the Fourier transform in https://en.wikipedia.org/wiki/Fourier_transform