  We consider an arbitrary finite-dimensional commutative associative algebra,
$\mathbb{A}_n^m$, with unit over the field of complex number with $m$
idempotents. Let $e_1=1,e_2,e_3$ be elements of $\mathbb{A}_n^m$ which are
linearly independent over the field of real numbers. We consider monogenic
(i.e. continuous and differentiable in the sense of Gateaux) functions of the
variable $xe_1+ye_2+ze_3$, where $x,y,z$ are real. For mentioned monogenic
function we prove curvilinear analogues of the Cauchy integral theorem, the
Morera theorem and the Cauchy integral formula.
