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You can add the keyword "hold" to integrate. Initial version:

sage: t=var('t')
sage: J(kk)=integrate(exp(-2*pi*I*kk*t),t,0,1)
sage: J(kk)
1/2*I*e^(-2*I*pi*kk)/(pi*kk) - 1/2*I/(pi*kk)

Note that the integral has already been computed. Instead:

sage: t=var('t')
sage: J(kk)=integrate(exp(-2*pi*I*kk*t),t,0,1, hold=True)
sage: J(kk)
integrate(e^(-2*I*pi*kk*t), t, 0, 1)
sage: J(0)
1