10. A function f defined on an interval I is called a step-function if and only if I can be subdivided into a finite number of subintervals I₁, I2, ..., I, such that f(x) = c₁ for all x interior to I, where the c₁, i = 1, 2, ..., n, are constants. Prove that every (x) step-function is integrable (whatever values f(x) has at the endpoints of the I) and find a formula for the value of the integral.