Virtual machine live migration, which migrates a virtual machine between data centers, is studied as a way to improve quality of services hosted on clouds. Meanwhile, traffic engineering is performed in networks that connect geographically-dispersed data centers. These two controls are originally designed and operated individually. Though it is naturally expected that integrating virtual machine live migration and the traffic engineering could result in a good overall performance, the effectiveness of such an integrated control has not been well understood. In this paper, we therefore quantitatively investigate its effectiveness. We first formulate an integrated control and an individual control as mixed integer programming problems in which the objective function is minimization of the average link delay in the network. Through numerical examples, we show that the integrated control can reduce the average link delay by at most 24 % and it can accommodate as 1.3 times much as incoming traffic compared with the individual control.