#### Answer

V = pi/3

#### Work Step by Step

Since pi is a constant, the formula you start off with is volume equals pi times the integral from zero to one of quantity -x + 1 squared. This can be rewritten as volume equals pi times integral of x^2 -2x +1.
V = pi * integral of (-x+1)^2 dx
V = pi * integral of ((x^2) -2x + 1 dx
V = pi * [((x^3)/3) - (x^2) + x]
V = pi * ((((1^3)/3 - (1^2) + 1) - (((0^3)/3) - (0^2) + 0))
V = pi *1/3
V = pi/3