This is not difficult to do; but you will need to create a bootable Ubuntu CD or USB, as you cannot edit or remove a partition you are currently using. Once you have done this, boot into it and open Gparted then delete the partition you no longer want. You can then right click on the other and expand it to fill the remaining space.
Reboot into Ubuntu and run
to remove the old Windows entry from your boot menu.
Resizing partitions always has the potential to cause data loss, although such loss is very unlikely.
Resizing and moving partitions CAN (depending on your exact partition layout) confuse GRUB and render your machine temporarily unbootable. This is easily fixed by using something like the Super Grub Disk to boot back into your machine, though that requires you having a separate working machine to create a Super Grub Disk with. You can then run sudo update-grub to restore normal booting.
Consider reinstalling Ubuntu over your entire disk, which will result in a cleaner system overall. This will, however, wipe all data on your disk.