The idea of integrated semigroup is associated with the study of the evolution equation (1) \(du/dt=Au\), where \(A\) does not satisfy all of the assumptions of the famous Hille-Yosida theorem. In such a setting integrating both sides of (1) from 0 to \(t\) we obtain a strongly continuous family of operators (not a semigroup) which is the integral of the semigroup from 0 to \(t\) in the case when \(A\) generates a semigroup. By this regard the family of operators in question is called the integrated semigroup. In the paper under review the idea described above is applied to the linear functional differential equation (2) \(dx/dt=L(x_ t)\). It is shown that the integrated semigroup associated with (2) can be extended to the space \(C\oplus\{X_ 0\}+R^ n\), where \(X_ 0\) is the matrix valued function defined by \(X_ 0(\theta)=0\) for \(\theta<0\) and \(X_ 0(0)=I\) (identity operator). Moreover, the technique of integrated semigroups is used to the case of nonhomogeneous delay differential equation \(dx/dt=L(x_ t)+f(t)\).