How to use Date Time Variable in Dynamic Query Salesforce

In some scenario you might have come across to fetch record with in some date time range. 
Here I am sharing some code for this. Suppose I am querying records from Minutes Object. There is two field Start_Time and End_Time present  in Minutes Object.
This is my page 

 <apex:inputField value="{!minute.Start_Time__c}" required="true" label="From Date"/>
 <apex:inputField value="{!minuteObj.End_Time__c}" required="true" label="To Date"/>
<apex:commandButton action="{!convertValidMinutesToUsage}" value="Process Minute's"/>

This is my controller 
public with sharing class ControllerValidMinutesToUsage {
     public Minute__c minute{get;set;}
     DateTime startDate;
     DateTime endDate;
     string query;

     public ControllerValidMinutesToUsage(){
            minute =  new Minute__c();
    }

    public void convertValidMinutesToUsage(){
       String sStartdate;
       String sEndDate;
       startDate = minute.Start_Time__c;
       sStartdate = startDate.format('yyyy-MM-dd\'T\'HH:mm:ss\'Z\'');
       endDate = minuteObj.End_Time__c+1;
       sEndDate = endDate.format('yyyy-MM-dd\'T\'HH:mm:ss\'Z\'');
       query = 'SELECT Start_Time__c ,End_Time__c, Is_Valid__c WHERE Is_Valid__c = false';
       query += ' AND Start_Time__c >='+sStartdate+' '+'AND Start_Time__c <='+sEndDate
       list<Minute__c> =  DateBase.query(query );
    }
}