Find the value of A^2

I have great difficulty reading this but it appears that you are integrating the function A (sin(2pi/L) x from 0 to L. That a rather trivial integral. Are you sure it isn't A sin((2pi/L) x)= A sin(2pi x/L)?

You also have "x" in your final answer. Since this is a definite integral, evaluated for x equal to the limits of integration, there should be no "x" in the result.

 

Your attachment is essentially unreadable. Why not adhere to PF standards and just type out the problem and your proposed solution?

 

Doing this would also help future readers, in case your picture gets deleted or something.

 

The ##X## is most likely an argument of the function ##\sin##, that is, it should be inside the brackets. Why are you studying quantum mechanics without doing calculus first? You should definitely study calculus before. This is the simplest math you'll encounter.

But answering your question:

https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus#Corollary

 

Once again, you have not completed the integral- evaluate it at the two limits of integration and subtract. After that it should be easy to solve the equation for A.