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In this article we prove the existence of solutions to the integrodifferential equation of mixed type x∆(t) = f (t, x(t), ∫0t k1(t, s)g(s, x(s))∆s, ∫0a k2(t, s)h(s, x(s))∆s), x(0) = x0, x0 ∈ E, t ∈ Ia = [0, a] ∩ T, a > 0, where T denotes a time scale (nonempty closed subset of real numbers R), Ia is a time scale interval. In the first part of this paper functions f, g, h are Carathéodory functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil delta integrals, which generalizes the Henstock-Kurzweil integrals. In the second part f, g, h, x are weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis delta integrals. Additionally, functions f, g, h satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness. [ABSTRACT FROM AUTHOR]