You don't install grub into an unused partition. You install it into the boot sector of your Ubuntu partition and let it handle Ubuntu kernel upgrades. The boot loader in the MBR (in my case it was Windows) doesn't boot Ubuntu kernel directly. Instead, it chain-loads grub in the Ubuntu partition. This way Ubuntu kernel upgrades are handled smoothly and transparently: Windows boot loader doesn't need to be updated each time you install a new Linux kernel.
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