Complex sentence: The Drive originated as the Harlem River Speedway, built from 1894 to 1898 and opened in July of that year, for the exclusive use of horse-drawn carriages and those on horseback--bicyclists were specifically excluded, as were sulkies and drays.
Split into simpler sentences: The Drive originated as the Harlem River Speedway, which started construction in 1894 and opened in July 1898. Originally, the Speedway was for the exclusive use of horse-drawn carriages and those on horseback; bicyclists were specifically excluded, as were sulkies and drays.