The invention provides a method of producing acrylic acid. The method includes contacting fumaric acid with a sufficient amount of ethylene in the presence of a cross-metathesis transformation catalyst to produce about two moles of acrylic acid per mole of fumaric acid. Also provided is an acrylate ester. The method includes contacting fumarate diester with a sufficient amount of ethylene in the presence of a cross-metathesis transformation catalyst to produce about two moles of acrylate ester per mole of fumarate diester. An integrated process for process for producing acrylic acid or acrylate ester is provided which couples bioproduction of fumaric acid with metathesis transformation. An acrylic acid and an acrylate ester production also is provided.