Let f:[0,1] to R be continuous function such that f(t) is greater or equal to 0 for all t in [0, 1].

Define g(x) = Integral f (t) dt ( integrated between 0 to x) then
1. g is monotone and bounded
2. g is monotone but not bounded
3. g is bounded but not monotone
4. g is neither monotone nor bounded

If f(x) is continous on[0,1]
then f is bounded on [0,1]
which implies g is bounded on [0,1].

Since f>=0 on [0,1], g(x) as defined
is a monotone increasing function of x.
This follows directly from a basic property
of the Rieman integral:
if 0<=x int{f(t)|t=0 to y}=int{f(t)|t=0 to x}
+int{f(t)|t=x to y}>=int{f(t)|t=0 to x}.

So the answer is 1.