Answer by Bob Hanlon for Solution doesn't have Kronecker delta

Clear["Global`*"]int[l_Integer, m_Integer] = Assuming[{l, m} ∈ Integers,  Piecewise[{     {Integrate[(2/Pi)*Cos[l x] Cos[m x] /. l -> m, {x, 0, Pi}],       l == m}},    Integrate[(2/Pi)*Cos[l x] Cos[m x], {x, 0, Pi}]] // Simplify]

Image may be NSFW.
Clik here to view.

Or,

Piecewise[Assuming[Element[{l, m}, Integers] && #,    {Simplify[Integrate[(2/Pi)*Cos[l x] Cos[m x], {x, 0, Pi}]], #}] & /@  {l == m, True}]

Image may be NSFW.
Clik here to view.