Battle of Waterloo
The Battle of Waterloo was fought on Sunday, 18 June 1815, near Waterloo in Belgium, part of the United Kingdom of the Netherlands at the time. A French army under the command of Napoleon Bonaparte was defeated by two of the armies of the Seventh Coalition: A British-led coalition consisting of units from the United Kingdom, the Netherlands, Hanover, Brunswick and Nassau, under the command of the Duke of Wellington, referred to by many authors as the Anglo-allied army or Wellington's army, and a Prussian army under the command of Field Marshal von Blücher, referred also as Blücher's army. The battle marked the end of the Napoleonic Wars.
Battle of Waterloo
Upon Napoleon's return to power in March 1815, many states that had opposed him formed the Seventh Coalition and began to mobilise armies. Wellington and Blücher's armies were cantoned close to the northeastern border of France. Napoleon planned to attack them separately in the hope of destroying them before they could join in a coordinated invasion of France with other members of the coalition. On 16 June, Napoleon successfully attacked the bulk of the Prussian army at the Battle of Ligny with his main force, causing the Prussians to withdraw northwards on 17 June, but parallel to Wellington and in good order. Napoleon sent a third of his forces to pursue the Prussians, which resulted in the separate Battle of Wavre with the Prussian rear-guard on 18–19 June, and prevented that French force from participating at Waterloo. Also on 16 June, a small portion of the French army contested the Battle of Quatre Bras with the Anglo-allied army. The Anglo-allied army held their ground on 16 June, but the withdrawal of the Prussians caused Wellington to withdraw north to Waterloo on 17 June.
I Cavalry Corps (Grande Armée)
The I Cavalry Corps of the "Grande Armée" was a French military unit that existed during the Napoleonic Wars.
I Cavalry Corps (Grande Armée)
For one month in 1806–1807, Emperor Napoleon I split his Reserve Cavalry Corps into the I and II Cavalry Corps. At that time, Marshal Joachim Murat took command of the short-lived I Cavalry Corps before resuming leadership over Napoleon's Reserve Cavalry when the experiment ended. The I Cavalry Corps was not recreated until 1812 for the invasion of Russia when command was exercised by General Étienne Marie Antoine Champion de Nansouty. The corps fought at Borodino and Tarutino. After being destroyed during the retreat from Russia, the I Cavalry Corps was reconstituted in 1813 and General Victor de Fay de La Tour-Maubourg was appointed to lead it. The corps fought at Lützen, Bautzen, Dresden, and Leipzig. At Leipzig, Latour-Maubourg was seriously wounded and replaced by General Jean-Pierre Doumerc who led the corps for the remainder of the War of the Sixth Coalition which ended with Napoleon's abdication in 1814. After Napoleon returned from exile and retook power in France in 1815, the main French Army was baptised as the "Armée du Nord". The army included the I Cavalry Corps led by General Pierre Claude Pajol which fought at Ligny and Wavre, while one detached division fought at Waterloo.

Question: I Cavalry Corps had a detached division that fought at the battle in which present-day country?
Answer: Belgium