what was the corrupt bargain and how did it affect the presidential election of 1824?
Actually, I don’t see any corruption in that election – just politics which involved legal and political precedence.
The following is also per http://en.wikipedia.org/wiki/United_States_presidential_election,_1824:
In the United States presidential election of 1824, John Quincy Adams was elected President on February 9, 1825, after the election was decided by the House of Representatives. This election is notable for being the only time since the passage of the Twelfth Amendment in which the presidential election was decided by the House of Representatives, as no candidate received a majority of the electoral vote. It is also often said to be the first election in which the president did not win the popular vote, although the popular vote was not measured nationwide. At that time, several states did not conduct a popular vote, allowing their state legislature to choose their electors.
The previous few years had seen a one-party government in the United States, as the Federalist Party had dissolved, leaving only the Democratic-Republican Party. In this election, the Democratic-Republican Party splintered as four separate candidates sought the presidency. Such splintering had not yet led to formal party organization, but later the faction led by Andrew Jackson would evolve into the Democratic Party, while the factions led by John Quincy Adams and Henry Clay would become the National Republican Party and later the Whig Party.
The election was partially a contest of favorite sons as it was a conflict over policy (positions on tariffs and internal improvements was where some significant disagreement existed), as the candidates were backed by different sections of the country: Adams was strong in the Northeast, Jackson in the South, West and mid-Atlantic, Clay in parts of the West, and Crawford in parts of the East.
John C. Calhoun of South Carolina, current Secretary of War, was initially a fifth candidate in the early stages of consideration, but he opted instead to seek the vice presidency and backed Jackson after seeing the popularity of Crawford in the South. Both Adams’ and Jackson’s supporters backed Calhoun, giving him an easy majority of electoral votes to be elected vice president.
[When] The presidential election was thrown to the U.S. House of Representatives. As per the Twelfth Amendment, only the top three candidates in the electoral vote were candidates in the House: Andrew Jackson, John Quincy Adams, and William Harris Crawford. Left out was Henry Clay, who happened to be Speaker of the House. Clay detested Jackson…Moreover, Clay’s American System was far closer to Adams’ position on tariffs and internal improvements than Jackson’s or Crawford’s, so Clay threw his support to Adams, who had many more votes than Clay.