Hi,
Let us consider this to be math problem. From the physics point of view the units are inconsistent:thus the problem is ill-posed.
What you need it to draw the graph pf the function y=cos(t^2), then the integration feature of the calculator to calculate the integral between 0 and some upper limit, which will be found by trial and error.
Here are some screen capture to help you along the way
Make sure the graph type is y=cos(X^2). Don<t worry the variable in this type of graph must be X
Choose the window to start at x=0
Here is your graph.
Press SHIFT F5 (G-Solv) You see the following image
Press F6 (Arrow pointing right) to access the other features, as on the following screen:
You see the integral sign above F3: Press F3 to do integration.
Use the left Arrow key to move the cross on the graph to X-0 or just enter 0. and press EXE. This is the lower bound.
You need to enter the upper bound. Since you do not know where to stop you must try different values and each time, read the value of the integral. For example if you enter Xupperlimit=0.5
the value of the integral is 0.45 (not 1)
Repeat the process changing the upper limit until (if you are lucky) you hit an integral of 1.
Now a few more pictures
Getting close. Now I use the 1st zero of the function, x=1.2533 approximate
Getting close. However from that zero to the next the area under the curve under the x-axis is negative and there will not be a solution until maybe somewhere in the second positive part.
So you can accept the value of the integral from X=0 to the 1st zero (1.2533) to be about 1. Or you will keep playing the game. But as the next picture shows, you will not get a better approximation than at the first zero.
Good Luck.