Yes, you do need to report your sales of RSU's.
They will be reported to the IRS by the broker they were sold through. And the IRS will be looking for those sales proceeds on your return.
Please go to the link below for further information about the sale of RSU's:
https://turbotax.intuit.com/tax-tools/tax-tips/General-Tax-Tips/How-to-Report-RSUs-or-Stock-Grants-o...