Int(phi(u-a*I)*exp(k*u*I),u = -infinity .. infinity);
  Change(%, u-a*I = s, s); subs(s=u,%): expand(%): combine(%,exp);

                   infinity
                  /
                 |
                 |          phi(u - a I) exp(k u I) du
                 |
                /
                  -infinity



                           infinity
                          /
                         |
              exp(-k a)  |          phi(u) exp(k u I) du
                         |
                        /
                          -infinity


however I think it should be

  Int(phi(u-a*I)*exp(k*u*I),u = lower .. upper);
  Change(%, u-a*I = s, s); subs(s=u,%): expand(%): combine(%,exp):
  subs(lower=-infinity, upper=infinity,%);


                        infinity - a I
                       /
                      |
           exp(-k a)  |                phi(u) exp(k u I) du
                      |
                     /
                       -infinity - a I