$a>1$
be an integer. Give a nonintegral expression in terms of $a$
for $F(a)=\displaystyle\int_1^a (1)^{\lfloor x \rfloor} \lfloor x \rfloor^{1} dx,$
where $\lfloor x\rfloor$
is the greatest integer less than or equal to $x.$

Sketch the graph
$y = \frac{1}{\lfloor{x}\rfloor}$
for$x > 1.$

How does multiplying it by
$(1)^{\lfloor{x}\rfloor}$
change the graph? 
An integral of a function is just the area under its graph.

Could you express the total area as a sum?

Plotting the function
$y = (1)^{\lfloor{x}\rfloor}\frac{1}{\lfloor{x}\rfloor}$
yields rectangles of width$1$
and height$1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots.$
Since an integral of a function is just the area under its graph,$F(a)=\sum_{i=1}^{a1}\frac{(1)^i}{i}.$