I have some confusion with this integral

exp(-k(2t-t-t))(t-t)dt= exp(-2k(t-t))

where exp(...) is the exponential function, the integration from 0 to t, k is a constant (and also t), (t-t) is Dirac delta function which equals 1 when t=t and zero when t≠t

can any one explain to me how this was done?