Integration - as in Enterprise Application Integration or EAI for short - addresses the need for various applications within an enterprise and outside, to communicate to each other.
Preferably, we want this integration to be seamless, reliable, and independent of platform and location.
We have several techniques and patters to achieve this, and as such the focus of EAI is on integration technology, on how to exchange information between applications.
The scope of SOA is much broader. Applications support (parts of) our processes, which are part of our end-to-end business processes, which are designed to achieve our business goals.
The aim of SOA is to optimally support business processes by implementing the various tasks within these processes as services that form the "lego stones" with which to build applications.
SOA integrates business processes, and it needs information integration and integration technology to do so. This makes EAI just one of the aspects of SOA.
The EAI approach per se completely ignores the big picture.