In Sage you need more steps.
Assuming that you need the exact and the approximate value:
var('x y')
s=solve([x^2+y^2-4==0,x+y-1==0],[x,y])
x0,x1=[sol[0].rhs() for sol in s]
assume(abs(x)<2)
ii=integrate(integrate(1,(y,1-x,sqrt(4-x^2))),(x,x0,x1))
#print ii
print ii.n()
#3.31871699805750
(The integration can be done numerically)
Andrzej Chrzeszczyk
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