Question

Show that the space R[a,b] of all Riemann integrable functions on the interval [a,b] is a linear space over a vector field R

Answer 1

$\int((f+g)(x))dx=\int f(x)dx+\int g(x)dx$

$\int(af(x))dx=a\int f(x)dx$

So, space R[a,b] of all Riemann integrable functions is a linear space.