The Riemann integral for vector-valued functions can be defined in the same way as for scalar-valued functions. Moreover, the theory of the so-defined integral is rather similar to the classical one.

Lewis, James T and Shisha, Oved 1983. The generalized Riemann, simple, dominated and improper integrals. Journal of Approximation Theory, Vol. 38, Issue. 2, p. 192.

Implementations of the following numerical integration techniques are given below: Left-hand Riemann sum, Right-hand Riemann sum, Midpoint Rule, Trapezoid Rule, and Simpson's Rule. Modify and evaluate ...

Integral calculus essentially deals with adding ... Later, mathematician Bernhard Riemann provided a more rigorous definition ...