to find the intersections of both curves, equalize and obtain the cut points
first it will be put in function of y
#x=5-y#
#x=y^2-4y+1#
equalize
#5-y=y^2-4y+1#
#0=y^2-3y-4#
factoring
#0=(y-4)(y+1)#
then #y=4 and y=-1#
now the area be
#A=int_-1^4(x_1-x_2)dy#
where #x_1=5-y# and #x_2=y^2-4y+1#
#A=int_-1^4(5-y-y^2+4y-1)dy#
#int_-1^4(5)dy=5(4)-5(-1)=25#
#-int_-1^4(y)dy=y^2/2 -> -((4)^2/2-(-1)^2/2)=-15/2#
#-int_-1^4(y^2)dy=y^3/3 -> -((4)^3/3-(-1)^3/3)=-65/3#
#int_-1^4(4y)dy=4(y^2/2) -> 4((4)^2/2-(-1)^2/2))=30#
#-int_-1^4(-1)dy=y->-(4-(-1))=-5#
#25-15/2-65/3+30-5=125/6#
#A=int_-1^4(5-y-y^2+4y-1)dy=125/6u^2#
