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import graph;
size(300,150,IgnoreAspect);
real f(real x) {return 1/x^(1.1);}
pair F(real x) {return (x,f(x));}
dotfactor=7;
void subinterval(real a, real b)
{
path g=box((a,0),(b,f(b)));
filldraw(g,lightgray);
draw(box((a,f(a)),(b,0)));
}
int a=1, b=9;
xaxis("$x$",0,b);
yaxis("$y$",0);
draw(graph(f,a,b,operator ..),red);
int n=2;
for(int i=a; i <= b; ++i) {
if(i < b) subinterval(i,i+1);
if(i <= n) labelx(i);
dot(F(i));
}
int i=n;
labelx("$\ldots$",++i);
labelx("$k$",++i);
labelx("$k+1$",++i);
labelx("$\ldots$",++i);
arrow("$f(x)$",F(i-1.5),NE,1.5cm,red,Margin(0,0.5));
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