What was Gottfried Wilhelm Leibniz’s contribution to the fundamental theorem of calculus?

Gottfried Wilhelm Leibniz independently discovered the fundamental theorem of calculus and published his findings in 1686, which contributed to a significant historical dispute regarding priority with Isaac Newton.12

Leibniz’s approach to the theorem was rooted in his development of a calculus of infinitesimals. He viewed the derivative as a quotient of infinitesimals ($df/dx$) and the integral as a sum of infinitesimal strips of area. Consequently, he interpreted the fundamental theorem as the relationship where the difference between successive sums is the last term in the sum: $d\int f(x)dx=f(x)dx$.1

Beyond the theorem itself, Leibniz provided a lasting contribution through his creation of appropriate mathematical symbolism. His notation, including the use of $d$ for difference and $\int$ for sum, remains the standard in modern mathematics and helped facilitate the widespread utility and calculation of calculus.1