{\displaystyle \int _{a}^{b}\!f(x)\,dx=F(b)-F(a).} The principles of integration were formulated independently by Isaac Newton and Gottfried Leibniz in the late 17th century, who thought of the integral as an infinite sum of rectangles of infinitesimal width.
amendment - a statement that is added to or revises or improves a proposal or document (a bill or constitution etc.) statement - a message that is stated or declared; a communication (oral or written) setting forth particulars or facts etc; according to his statement he was in London on that day.
An amendment is a change or addition to a contract after it has been ratified. Case in point is the example of our country's Constitution. The constitution was written as a contract between the first 13 states. James Madison promised to incorporate a Bill of Rights once the Constitution was ratified. Upon ratification of the constitution, the first 10 amendments were written.