Integral

An integral is an operator that assigns to a function another function representing the accumulation of its values of a domain; formally, for a real-valued function $f$ on $[a,b]$, the definite integral

$${\int }_a^{b}f(x)dx$$

is the limit of Riemann sums and equals the net area under $f$ on $[a,b]$, while the indefinite integral

$$\int f(x)dx$$

denotes the family of antiderivatives of $f$.