First, your example references the x-axis; not the y-axis. Here's how to plot a portion of the data along the x axis. The same process can be applied to the y-axis.
load sunspot.dat
year = sunspot(:,1);
avSpots = sunspot(:,2);
% select the data you want to include
%'includeIndex' is a logical index that selects which data to include
% This statement selects any data between 1750-1800 and 1850-1900
Yeah, that's very very easy to do. Check out the how I formed the "idx1" or "idx2" variables - you'll do the same except with the years you listed above. To get the starting year, min(year). To get the end year, max(year).
You can also select a web site from the following list
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.