  Let $B\subset A$ be a left or right bounded extension of finite dimensional
algebras. We use the Jacobi-Zariski long nearly exact sequence to show that $B$
satisfies Han's conjecture if and only if $A$ does, regardless if the extension
splits or not. We provide conditions ensuring that an extension by arrows and
relations is left or right bounded. Finally we give a structure result for
extensions of an algebra given by a quiver and admissible relations, and
examples of non split left or right bounded extensions.
