Do I just straight up integrate (x + cosx)? <--- yes
and to change my interval do I plug Pi/2 and Pi/3 to cos(x)??<--- no, you have to replace x by pi/2 and pi/3 respectively
awesome... so we didn't have to change the interval of Pi/2 and Pi/3, because usually that's what I'm used to doing..... So since we can't further simplify this equation we just leave it as it is??
Sometimes when I'm doing a substitution on a definite integral, I'll write so that I remember to change the limits of integration when I do the substitution.