{\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.
Change in a legal document made by adding, altering, or omitting a certain part or term. Amended documents, when properly executed (signed by all parties concerned), retain the legal validity of the original document. For construction or supply contracts, amendment refers to change made before the contract is awarded, any change made afterwards is called modification. The salesman made an amendment to agreed car lease stating that the buyer would not have to pay the first months payment which was originally mandatory in the lease.