In this paper, we develop a conceptual design of optimal integrated processes for the production of dimethyl furfural (DMF) and furfural from biomass, switchgrass and algae. The processes consist of four stages: (1) biomass pretreatment into intermediates such as oil and glucose from algae and glucose and xylose from switchgrass; (2) dehydration of the sugars; (3) hydroxymethyl furfural (HMF) and furfural purification; (4) synthesis of DMF out of HMF and fatty acid ethyl ester (FREE) from oil in the case of using algae. We formulate mixed-integer nonlinear programming models so as to simultaneously optimize and heat integrate the processing of both raw materials. For switchgrass, the use of Ammonia Fiber Explosion (AFEX) pretreatment is recommended for a production of cost of DMF and furfural of $3/kg ($570 MM of fixed investment cost). For algae, the composition, is 60% oil, 30% starch, and 10% protein to obtain 98 MMgal/yr of biofuels, 16% of DMF, at a cost of $1.98/gal ($693 MM of fixed investment). If the sugar concentration in the dehydration reactor increases from 10 to 30%, we can reduce the production costs by 25% and the investment costs up to 50%.