While as an educator, I'd like to think that my students, by studying moral issues and learning to sympathize with diverse peoples and cultures, will not become corrupt officials, realistically, whether individuals are or are not corrupt, in the sense of cheating or taking bribes, depends more on their moral values and circumstances than their educations. On the other hand, well-educated societies, as a whole, have less of a culture of impunity and corruption than less well educated societies.
The first reason is that it is much harder to cheat or bully well-educated members of the middle class than people who are poor or only marginally literate. Second, well-educated societies do have a broad middle class rather than a powerful entitled elite and disempowered people living in rural poverty with no recourse in dealing with corrupt officials. Well-educated societies are likely to have active media making inquiries into corruption and publicizing official corruption. Having strong and independent media, whether newspapers or blogs, discourages corruption, but for media to be effective, the audience needs to be literate and sufficiently well off to have access to print or web media.
That being said, many multinational corporations led by people from the top universities in the world have been caught giving bribes to public officials. Even in the United States, which is a wealthy and well educated country, many large corporations have shown to be morally corrupt, just staying on the right side of the letter of anti-corruption laws while dodging taxes, hiring ex-politicians as "consultants, and taking advantage of their less-well paid employees.