Answer:
V = 1/6 cubic units
Step-by-step explanation:
Applying the concept of integrals for volume calculation:
 (1)
          (1)
V = volume of the solid bounded by x = a and x = b
S(x) = cross section area of the solid, perpendicular to the x axis
From the figure we have that S is the area of a triangle that has base Z and height Y
Area of the triangle =  (2)
          (2)
Calculation of y(x) and z(x)
We apply the equation of the point-slope line (plane xy):
Slope =  (3)
          (3)
Equation of the line =  (4)
          (4)
Replacing the points (1,0) and (0,1) in (3):

Replacing the point (1,0) and m = -1 in (4):

y(x) = -x + 1 (Line A-B)          (5)
We apply the equation of the point-slope line (plane xz):
Slope =  (6)
          (6)
Equation of the line =  (7)
          (7)
Replacing the points (1,0) and (0,1) in (6):

Replacing the point (1,0) and m = -1 in (7):

z(x) = -x + 1 (Line A-C)        (8)
Replacing (5) and (8) in (2)
 (9)
          (9)
Replacing (9) in (1) and knowing that a = 0 and b = 1:

 evaluated from x=0 to x=1
  evaluated from x=0 to x=1
