Graph limits and area

I have the following code:

x = linspace(-5, 5, 1000);
y1 = -x;
y2 = x.^2-4;
lidx = y1 >= y2;
figure
set(findobj(gcf,'type','axes'),'FontName','Arial','FontSize',12,'FontWeight','Bold', 'LineWidth', 2);
plot(x, y1, 'k')
hold on
plot(x, y2, 'k')
patch([x(lidx) fliplr(x(lidx))], [y1(lidx), fliplr(y2(lidx))], 'b', 'FaceAlpha', 0.4)   
hold off 
xlim([-5 5])
ylim([-5 5])
box on
grid on
axis=gca;
axis.XAxisLocation = 'origin';
axis.YAxisLocation = 'origin';
title('Graph of the integration domain')

xlabel('x')
ylabel('y')

which gives the following graph. Is there a way of putting dashed lines where the green line is to show limits and to reduce the blue patch within the area. Thank you.

[KSSV]

Get those intersection points and use patch.