Systems integrating heterogeneous processors with unified memory provide seamless integration among these processors with minimal development complexity. These systems integrate accelerators such as GPUs on the same die with CPU cores to accommodate running parallel applications with varying levels of parallelism. Such integration is becoming very common on modern chip architectures, and it places a burden (or opportunity) on application and system programmers to utilize the full potential of such integrated chips. In this paper we evaluate whether we can obtain any performance benefits from running garbage collection on integrated GPU systems, and discuss how difficult it would be to realize these gains for the programmer. Proliferation of garbage-collected languages running on a variety of platforms from handheld mobile devices to data centers makes garbage collection an interesting target to examine on such platforms and can offer valuable lessons for other applications. We present our analysis of running garbage collection on integrated systems and find that the current state of these systems does not provide an advantage for accelerating such a task. We build a framework that allows us to offload garbage collection tasks on integrated GPU systems from within the JVM. We identify dominant phases of garbage collection and study the viability of offloading them to the integrated GPU. We show that performance advantages are limited, partly because an integrated GPU has limited advantage in memory bandwidth over the CPU, and partly because of costly atomic operations.