We provide a method to calculate the integrations of some augmentations over finite-dimensional algebras, and prove that these integrations are Bochner integrations. Furthermore, let Λ be an algebra of type 𝔸t, we show that there exists a Nakayama algebra Λ' of type $${\vec{\mathbb{A}}_t\,=\,1{\longrightarrow}\,2\,{\longrightarrow}\,{\cdots}\,{\longrightarrow}\,t$$ such that the number ♯(mod(Λ)) of isoclasses of indecomposable right Λ-modules, the dimension dim Λ' of the Nakayama algebra Λ' as a vector space, and the Bochner integrations (B) $\int{_{[0,1]^{{\times}t}}}\;2{\sum}_{i=1}^{t}\,\text{v}_p_i\,d{\mu}$ coincide. Here, p1, . . . , pt are all right maximal paths on the bound quiver of Λ', and, for each 1 ⩽ i ⩽ t, vpi is the sum of all augmentations vv corresponding to starting points v of all arrows on pi. Moreover, we consider some algebras of type 𝔻 by a similar way.