Question 941581
the graph of y = -x +6 forms a triangle with the x and y axis intersection points, see graph below
{{{ graph( 300, 200, -10, 10, -10, 10, -x +6) }}}
the y axis intercept is (0, 6) and the x axis intercept is (6, 0)
integral of  -x +6  =  (-x^2/2) + 6x
to determine the area under the curve, we evaluate the integral at x = 0 and x = 6
integral = 0 at x=0
integral = -18 + 36 = 18 at x = 6
Area = 18 - 0 = 18
we can check our answer by using area of triangle formula
Area = (1/2) * b * h = (1/2) * 6 * 6 = 18
our answer checks